Background Noise Cancellation for Acoustic Detection of Manatee Vocalizations

Home , Background noise, Noise reduction

BACKGROUND NOISE CANCELLATION FOR ACOUSTIC DETECTION OF MANATEE VOCALIZATIONS

ZHENG YAN

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2006

Zheng Yan

To my family

ACKNOWLEDGMENTS

The author would like to express his great gratitude to his advisors, Dr. Christopher

Niezrecki and Dr. Louis Cattafesta, for suggesting the topic of this work, providing continuous guidance, support and encouragement throughout this research.

The author would like to thank Dr. Jose Principe for his guidance and advice from the committee members, Dr. John Harris and Dr. Richard Lind. The author also would like to thank his fellow students in the Smart Structures and Acoustic Laboratory and

Interdisciplinary Microsystems Group (IMG) for sharing their knowledge.

The author would like to express his sincere appreciation to the Florida Sea Grant,

Florida Fish and Wildlife Conservation Commission, and University of Florida Marine

Mammal Program in supporting this research.

Finally, the author gives special appreciation to my family, for their love, patience, and support.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... iv

TABLE OF CONTENTS...... v

LIST OF TABLES...... viii

LIST OF FIGURES ...... ix

NOMENCLATURE ...... xvii

ABSTRACT...... xx

CHAPTER

1 INTRODUCTION ...... 1

Need for Manatee Detection System ...... 1 Why Manatees Collide With Boats ...... 3 Contributions ...... 5 Organization of the Dissertation...... 7

2 RESEARCH BACKGROUND AND REVIEW OF DETECTION METHODS ...... 11

Manatee Detection Methods...... 12 Acoustic Detection of Manatee Vocalizations ...... 14 Vocalizations and Behavior of Manatees...... 14 Major Background Noise ...... 18 Comparison Between Manatee Calls and Dolphin Calls ...... 20 Other Methods of Acoustic Detection ...... 21 Matched Filtering ...... 22 Hidden Markov Model (HMM)...... 22 Artificial Neural Networks (ANN)...... 23 Spectrogram Correlation ...... 23

3 REVIEW OF BACKGROUND NOISE CANCELLATION...... 25

Adaptive Noise Cancellation (ANC)...... 26 Feedforward ANC ...... 26 Feedback ANC ...... 27

v ANC for Underwater Acoustics ...... 27 ANC without Reference Input...... 29 ANC Structures ...... 30 Blind Signal Separation (BSS) ...... 31 Wavelet-Based Noise Reduction ...... 34 Conclusions...... 36

4 ADAPTIVE LINE ENHANCER (ALE)...... 37

General Adaptive Filter ...... 37 Wiener Filter...... 38 Least Mean Square (LMS) ...... 40 Limitations of the LMS Algorithm and ANC System...... 41 Theory of FIR-ALE ...... 44 Theory of IIR-ALE...... 46 Review of ALE...... 48 FIR Structure ALE ...... 48 IIR Structure ALE ...... 50 Feedback Adaptive Line Enhancer (FALE) ...... 52

5 ESTABLISHMENT OF THE MANATEE LIBRARY ...... 55

6 SIMULATION RESULTS AND ANALYSES...... 59

Signal Preprocessing...... 59 Parameter Selection of ALE ...... 60 Review of Delay Parameter...... 60 Delay Parameter for Manatee Problem ...... 63 Review of Optimal Order and Step Size ...... 66 Order for Manatee Problem...... 67 Variable Step Size ALE...... 70 Feedback Constant...... 71 Simulation Results in Time Domain...... 72 Simulation Results in Terms of SNR...... 77 Results on Acoustic Superposition of Manatee Vocalizations...... 90 Field Test ...... 92 Description of Field Test...... 92 Conversion From Spherical to Mixed Spreading ...... 94 Simulation Results...... 95

7 PERFORMANCE COMPARISON BETWEEN FIR-ALE AND FALE ...... 103

Computational Complexity...... 103 FIR-ALE...... 103 FALE ...... 104 Stability...... 106 Convergence Rate and Tracking Ability ...... 107

vi Advantage and Disadvantage of FIR-ALE and FALE...... 110

8 DETECTION RANGE ESTIMATION...... 113

Theoretical Development...... 113 Estimation of Improved Detection Range ...... 115 Estimation of the Improved Detection Range ...... 122 SPL of Manatee Vocalizations and Background Noise ...... 122 Estimation of Detection Range (bandpass filter)...... 123 Estimation of Detection Range (FIR-ALE)...... 125 Estimation of Detection Range (FALE)...... 125

9 REAL TIME SIMULATION ...... 133

Experimental Laboratory Setup...... 134 Simulink Block Diagrams and Implementation ...... 134 dSPACE Layout...... 139 Simulation Results...... 141

10 CONCLUSIONS AND FUTURE WORK...... 146

Conclusions...... 146 Future Work...... 147

APPENDIX

A OPTIMAL DELAY PARAMETER OF ALE...... 150

Evaluation Criterion...... 151 One Sinusoid Corrupted by White Noise ...... 153 Two Sinusoids Corrupted by White Noise ...... 155 Three Sinusoids Corrupted by White Noise ...... 156 Common Characteristics for These Three Cases...... 157 Proposed Performance Evaluation Criterion ...... 160 Conclusions...... 162

B MANATEE VOCALIZATIONS IN THE LIBRARY...... 163

LIST OF REFERENCES...... 174

BIOGRAPHICAL SKETCH ...... 184

vii

LIST OF TABLES

Table page

6-1. Parameters of ALE (FIR-ALE and FALE) for the simulations...... 72

6-2. The average performance of bandpass filter, FIR-ALE and FALE for the manatee calls corresponding to each category (dB)...... 83

7-1. Computational complexity of FIR-ALE...... 104

7-2. Computational complexity of FALE...... 105

9-1. Description of tracks used for testing...... 142

9-2. Detection results of the system without noise reduction for each track ...... 143

9-3. Detection results of the system with noise reduction for each track ...... 144

9-4. Results of the comparison between the system without and with noise reduction...145

viii

LIST OF FIGURES

Figure page

1-1. Manatee surfacing for air...... 2

1-2. Number of manatee deaths from watercraft collisions from 1976 to 2001 and percentage breakdown of total manatee deaths...... 2

1-3. Alert sign and boater in manatee zone...... 3

2-1. Conceptual sketch of manatee warning system...... 15

2-2. Frequency spectrum of a typical manatee vocalization...... 17

2-3. Spectrogram of typical manatee vocalizations...... 17

2-4. Typical snapping shrimp noise in time domain...... 19

2-5. Frequency spectrum of typical boat noise ...... 20

2-6. Frequency spectrum of natural noise...... 20

2-7. Spectrogram of three typical dolphin whistles...... 21

3-1. Broadband feedforward ANC system...... 26

3-2. Illustration of blind signal separation...... 32

3-3. Herault-Jutten method for blind signal separation...... 33

4-1. Block diagram of Wiener filter...... 39

4-2. Simplified block diagram of adaptive noise canceller based on LMS algorithm...... 41

4-3. Block diagram of an ANC system under realistic conditions...... 43

4-4. Block diagram of FIR-ALE...... 44

4-5. Block diagram of IIR-ALE...... 47

4-6. The relationship between the SNR of input and the gain of ALE...... 49

ix 4-7. Block Diagram of Feedback Adaptive Line Enhancer (FALE)...... 53

5-1. The procedure of classifying manatee calls...... 57

6-1. Autocorrelation of manatee vocalizations and background noise. (a) pure manatee vocalization, (b) natural noise and (c) boat noise...... 66

6-2. Power spectrum of a typical manatee vocalization (from category 1110)...... 68

6-3. The instantaneous transfer function of FIR-ALE during the manatee call period when the order of adaptive filter is set to 70...... 68

6-4. The instantaneous transfer function of FIR-ALE during the manatee call period when the order of adaptive filter is set to 20...... 69

6-5. The instantaneous transfer function of FIR-ALE outside the period of the manatee call when the order of adaptive filter is set to 20...... 70

6-6. Manatee vocalizations and background noise in time domain. (a) pure manatee vocalizations, (b) natural noise, (c) boat dominated noise, (d) snapping shrimp noise and (e) superposition of manatee calls, natural noise, boat dominated noise, and snapping shrimp noise...... 73

6-7. Performance of bandpass filter, FIR-ALE, and FALE in time domain. (a) after the band pass filter is applied, (b) after FIR-ALE is applied and (c) after FALE is applied...... 74

6-8. Spectrogram of the five original manatee calls...... 75

6-9. Spectrogram of the manatee calls after band pass filter is applied...... 76

6-10. Spectrogram of the manatee calls after FIR-ALE is applied...... 76

6-11. Spectrogram of the manatee calls after FALE is applied...... 76

6-12. The method used to compute the SNR of an original manatee call. (a) pure manatee call and (b) background noise...... 78

6-13. The method used to compute the SNR of the manatee call after filtering. (a) superposed signal of pure manatee call and background noise after FALE is applied and (b) background noise after FALE is applied...... 78

6-14. SNR of each manatee vocalization after band pass filter is applied when SNR ori is equal to -5 dB...... 79

6-15. SNR of each manatee vocalization after FIR-ALE is applied when is SNR ori equal to -5 dB...... 80

x 6-16. SNR of each manatee vocalization after FALE is applied when is equal SNR ori to -5 dB...... 80

6-17. SNR improvement of the FALE compared to FIR-ALE for each manatee vocalization when is equal to -5 dB...... 81 SNR ori

6-18. Percentage for which the performance of FALE is worse than that of FIR-ALE....81

6-19. Performance of bandpass filter, FIR-ALE, and FALE. (a) SNR of manatee calls after band pass filter is applied for each category and various SNR, (b) SNR of manatee calls after FIR-ALE is applied for each category and various SNR and (c) SNR of manatee calls after FALE is applied for each category and various SNR...... 84

6-20. Upper bound of overall performance comparison between the band pass filter, FIR-ALE, and FALE as a function of the SNR...... 86

6-21. Performance gains of the various algorithms using the same band pass filter as a baseline as a function of the SNR for the upper bound case...... 86

6-22. Lower bound for overall performance comparison between the bandpass filter, FIR-ALE, and FALE as a function of the SNR of the original manatee call...... 87

6-23. Performance gains of the various algorithms using the same bandpass filter as a baseline as a function of the SNR for lower bound case...... 88

6-24. Lower bound and upper bound for the performance of bandpass filter, FIR-ALE, and FALE...... 88

6-25. Lower bound of the performance of the bandpass filter, FIR-ALE and FALE with the delay from 10 to 3000 when the SNR of original manatee vocalizations is -5 dB...... 89

6-26. Upper bound of the performance of the bandpass filter, FIR-ALE and FALE with the delay from 10 to 3000 when the SNR of original manatee vocalizations is -5 dB...... 89

6-27. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and high-level background noise. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 90

6-28. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and low-level background noise. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 91

xi 6-29. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 5 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 96

6-30. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 25 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 97

6-31. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 50 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 98

6-32. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 75 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 99

6-33. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 100 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 100

6-34. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 5 ft and manatee vocalizations is located at 5 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 101

6-35. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 5 ft and manatee vocalizations is located at 25 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied...... 102

7-1. Gain growth trajectories of FALE with fixed β , FALE with exponential β , and FIR structure ALE for extracting a single sinusoid from white noise...... 109

7-2. Lower bound for overall performance of FIR-ALE as a function of the SNR of the original manatee call for different step sizes...... 111

xii 7-3 Lower bound for overall performance of FALE as a function of the SNR of the original manatee call for different step sizes...... 111

7-4. Improvement of FALE over FIR-ALE for different step sizes...... 112

8-1. Illustration of the manatee detection...... 116

8-2. Lower bound of the overall performance comparison between the bandpass filter, FIR-ALE, and FALE as a function of the SNR of the manatee vocalizations after bandpass filtering ...... 117

8-3. Curve fittings for the performance of FIR-ALE and FALE...... 119

8-4. Lower bound for the relationship between the ratio of R2/R1 and the lowest

SNR BPF (lower bound) that the system can detect a vocalization by only using a bandpass filter...... 120

8-5. Curve fitting for upper bound of the performance of FIR-ALE and FALE...... 121

8-6. Upper bound for the relationship between the ratio of R2/R1 and the lowest SNRBPF (lower bound) that the system can detect a vocalization by only using a bandpass filter...... 121

8-7. Overall comparison between the lower bound and upper bound of FIR-ALE and FALE...... 122

8-8. Maximum manatee detection ranges at NL =70 dB and SLB =125 dB only using a bandpass filter...... 126

8-9. Maximum manatee detection ranges at NL =80 dB and SLB =125 dB only using a bandpass filter...... 127

8-10. Maximum manatee detection ranges at NL =90 dB and SLB =125 dB only using a bandpass filter...... 127

8-11. Maximum manatee detection ranges at NL =100 dB and SLB =125 dB only using a bandpass filter...... 128

8-12. Maximum manatee detection ranges at NL =70 dB and SLB =125 dB after FIR- ALE is applied...... 128

8-13. Maximum manatee detection ranges at NL =80 dB and SLB =125 dB after FIR- ALE is applied...... 129

8-14. Maximum manatee detection ranges at NL =90 dB and SLB =125 dB after FIR- ALE is applied...... 129

xiii 8-15. Maximum manatee detection ranges at NL =100 dB and SLB =125 dB after FIR- ALE is applied...... 130

8-16. Maximum manatee detection ranges at NL =70 dB and SLB =125 dB after FALE is applied...... 130

8-17. Maximum manatee detection ranges at NL =80 dB and SLB =125 dB after FALE is applied...... 131

8-18. Maximum manatee detection ranges at NL =90 dB and SLB =125 dB after FALE is applied...... 131

8-19. Maximum manatee detection ranges at NL =100 dB and SLB =125 dB after FALE is applied...... 132

9-1. Experimental laboratory setup...... 134

9-2. Simulink block diagrams of the real time simulations...... 135

9-3. ALE algorithm subsystem block...... 136

9-4. Block parameters of ALE...... 136

9-5. LMS algorithm subsystem block...... 137

9-6. Detection block with threshold detection method...... 137

9-7. Time delay subsystem block...... 138

9-8. Counter subsystem block...... 139

9-9. System counter and user counter subsystem block...... 139

9-10. User interface of real time simulation in dSPACE when only noise is present. ....140

9-11. The interface of the real time simulation in dSPACE when a manatee vocalization is present...... 141

9-12. Detection results of the system without noise reduction for each track...... 143

9-13. Detection results of the system with noise reduction for each track...... 144

9-14. Overall performance comparison between FIR-ALE and bandpass filter...... 145

A-1. Frequency spectrum of normalized H ()ω when delay =13 and order =18...... 152

A-2. Frequency spectrum of normalized G()ω when delay =13 and order =18...... 153

xiv A-3. Frequency spectrum of normalized G()ω when delay= 1 and 16 and order=9.....154

A-4. Frequency spectrums of normalized G()ω with delay of 1 and 6 and order=9.....155

A-5. Frequency spectrum of normalized G()ω when delay= 1 and 8 and order=15.....156

A-6. Frequency spectrum of normalized G()ω when delay = 1 and 10 and order =15.157

A-7. Frequency spectrum of G()ω when delay =6 and order =9...... 158

A-8. Frequency spectrum of normalized G()ω when delay =15 and order =9...... 158

A-9. Frequency spectrum of normalized G()ω when delay =18 and order=20...... 159

A-10. Frequency spectrum of normalized G()ω with delay of 8 and 28...... 159

A-11. SNR after FIR-ALE is applied for the delay from 1 to 100 when order =15...... 160

A-12. SNR after ALE with different delay when SNR before ALE is 0 dB ...... 161

A-13. The relationship between ∆PL, , and δω ...... 162

B-1. Manatee vocalizations from category 0000 in time domain...... 164

B-2. Spectrogram of manatee vocalizations from category 0000...... 164

B-3. Manatee vocalizations from category 1000 in time domain...... 165

B-4. Spectrogram of manatee vocalizations from category 1000...... 165

B-5. Manatee vocalizations from category 1010 in time domain...... 166

B-6. Spectrogram of manatee vocalizations from category 1010...... 166

B-7. Manatee vocalizations from category 1011 in time domain...... 167

B-8. Spectrogram of manatee vocalizations from category 1011...... 167

B-9. Manatee vocalizations from category 1100 in time domain...... 168

B-10. Spectrogram of manatee vocalizations from category 1100...... 168

B-11. Manatee vocalizations from category 1110 in time domain...... 169

B-12. Spectrogram of manatee vocalizations from category 1110...... 169

xv B-13. Manatee vocalizations from category 1111 in time domain...... 170

B-14. Spectrogram of manatee vocalizations from category 1111...... 170

B-15. Manatee vocalizations from category 1200 in time domain...... 171

B-16. Spectrogram of manatee vocalizations from category 1200...... 171

B-17. Manatee vocalizations from category 1210 in time domain...... 172

B-18. Spectrogram of manatee vocalizations from category 1210...... 172

B-19. Manatee vocalizations from category 1211 in time domain...... 173

B-20. Spectrogram of manatee vocalizations from category 1211...... 173

xvi

NOMENCLATURE

∆ Delay of ALE

µ Step size of the adaptive filter

β Feedback constant

ω0 Natural frequency of second order system

A Weights of the adaptive filter

AG Array Gain

DI Directivity Index

DT Detection Threshold

L Order of the adaptive filter

M Misadjustment of the adaptive filter

NL Ambient Noise Level

R Distance from the source with reference to 1 m

R1 Maximum distance that the manatee is detectable without

background noise cancellation

R2 Maximum distance that the manatee is detectable using

background noise cancellation

RB Distance of the boat from the hydrophone

RM Maximum distance a manatee is detectable

RN Received Boat Noise

xvii SE Signal Excess

SL Source Level

SLB Source Level of the Boat

SLM Source Level of the Manatee vocalization

TL Transmission Loss

TLB Transmission Loss of the Boat

ALE Adaptive Line Enhancer

ANC Adaptive Noise Cancellation

ANN Artificial Neural Network

ARMA Autoregressive Moving Average

AUV Autonomous Underwater Vehicles

BIBO Bound-Input Bound-Output

BSS Blind Signal Separation

FALE Feedback Adaptive Line Enhancer

FIR Finite impulse response

FIR-ALE FIR structure ALE

FOM Figure of Merit

HMM Hidden Markov Model

IIR Infinite impulse response

IIR-ALE IIR structure ALE

LMS Least Mean Square

MSE Mean Square Error

RLS Recursive Least Square

xviii RMS Root Mean Square

ROC Receiver Operating Characteristic (also Receiver Operating Curve)

SNR Signal to Noise Ratio

SPL Sound Pressure Level

TDL Tapped Delay Line

xix

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

BACKGROUND NOISE CANCELLATION FOR ACOUSTIC DETECTION OF MANATEE VOCALIZATIONS

Zheng Yan

August, 2006

Chair: Christopher Niezrecki Cochair: Louis N. Cattafesta III Major Department: Mechanical and Aerospace Engineering

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of an increase in the number of collisions with boats. A device is desired to alert boaters of the presence of manatees, so that a collision can be avoided. The practical implementation of the technology is dependent on the hydrophone spacing and the range of detection. These parameters are primarily dependent on the manatee vocalization strength, the decay of the signal’s strength with distance, and the background noise levels. An efficient method to extend the detection range by using background noise cancellation is proposed in this dissertation.

A Finite Impulse Response (FIR) structure and a constrained Infinite Impulse

Response (IIR) structure Adaptive Line Enhancer (ALE), called Feedback ALE (FALE), that can detect and track narrowband signals buried in broadband noise are implemented in MATLABTM to reduce the background noise. A library consisting of 100 manatee calls spanning ten different signal categories is established and used to evaluate the

xx performance of the FIR-ALE and FALE with a bandpass filter acting as a baseline for comparison. A proper range of the delay for the FIR-ALE and FALE is given based on the manatee vocalizations in the established library. A field test is performed to evaluate the performance of these three algorithms in time domain using an acoustic superposition of manatee vocalizations and background noise.

The improvement of the detection range of the system enhanced by ALE over bandpass filter is estimated with lower and upper bounds. The improved detection range is also estimated using the lower bound of the performance of ALE. A real time system is developed using dSPACE. The performance of ALE is further evaluated in terms of correct detections, false detections, and missed calls. The improved SNR of manatee vocalizations may be used to extend the range of detection of manatee vocalizations and reduce the false alarm and missed detection rate during implementation of the system in the manatee’s natural habitat.

xxi CHAPTER 1 INTRODUCTION

This dissertation addresses one aspect of the general problem of enhancing a signal that has been corrupted by an additive noise. While the research described in this dissertation focuses on the specific application of removing background noise (such as boat noise and shrimp snapping) from a manatee call, the results are readily extendible to other applications in which a signal needs to be enhanced by reducing the additive noise.

The need for a manatee detection system is first described in this chapter. Then, the reasons why manatees collide with boats are given. Finally, the organization and contributions of the dissertation are presented.

Need for Manatee Detection System

In recent years, the West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of a growing number of fatal collisions with boats

(Gerstein, 2002). A manatee surfacing for air is shown in Figure 1-1. The number of manatee deaths caused by collisions with watercraft per year from 1976 to 2001 is shown in Figure 1-2 (Gerstein, 2002). It can be seen that 36% of all manatee deaths are caused by collisions with watercraft. The reason why these collisions occur will be discussed in the next section. The warmer bodies of water can be dangerous for manatees because many of them are also popular locations for boating and water recreation. The collisions with boats have resulted in a large number of manatee deaths and injuries, resulting in an increased number of boater “idle-speed” or “no-wake” zones within the waters of the southeastern United States.

1 2

Figure 1-1. Manatee surfacing for air.

Figure 1-2. Number of manatee deaths from watercraft collisions from 1976 to 2001 and percentage breakdown of total manatee deaths.

A sign to alert boaters in manatee zone is shown in Figure 1-3. These zones are responsible for causing conflicts between boaters and people interested in protecting manatees. Boaters want fewer restrictions on the waterways so that they can use it for commercial and recreational purposes. The number of manatee deaths is so great that the

Endangered Species Act of 1973 classifies the manatee as a species “in danger of extinction without human protection.” It is of great interest to the general public to investigate the reasons why manatees collide with boats and eliminate the number of collisions between manatees and boats as well as easing boating restrictions in manatee

3 areas. If people can easily detect manatees’ presence in the water, it may be possible to reduce or eliminate collisions that watercraft have with these animals.

Figure 1-3. Alert sign and boater in manatee zone.

Why Manatees Collide With Boats

Between 1995 and 2002 the percentage of mortalities of the West Indian manatee due to watercraft strikes has risen from 22% to 31% (Florida Department of

Environmental Protection, Division of Marine Resources, 1996; Florida Fish and Wildlife

Conservation Commission, 2002). The increase in the number of collisions is caused by several factors. Certainly, the increase in human activity within manatee areas is directly related to the number of collisions. According to the United States Coast Guard, the number of registered boats in Florida has grown to over 900,000 as of 2001 (United

States Coast Guard, 2002) and is continually increasing. Another reason is that the population of the West Indian manatee has also increased slightly in recent years, reaching an estimated population of 3,276.

The establishment of “idle-speed” zones is based on the assumption that manatees could readily hear as well as locate the sounds of slow-moving boats. In order to avoid the boats, manatees must be able to hear and locate the boats. For manatees, as for other

4 animals, the ability to hear and localize sounds is critical to their survival. These collisions have led to the testing of the hearing capabilities of manatees and to research into their behavioral response in the presence of boats (Gerstein, 2002; Nowacek et al.,

2004).

It has been postulated that these collisions occur partly because manatees cannot hear approaching boats at low frequencies. Gerstein et al. (1999) studied the hearing of manatees and created the first manatee audiogram. His continuous research suggests that manatees’ hearing is the most sensitive in a frequency range between 16 and 18 kHz, and not 1 kHz to 5 kHz as previously thought (Bullock et al., 1982; Gerstein, 2002).

Unfortunately, the main energy of boat noise is focused in the low frequency range where the hearing of manatees is poor. Secondly, the physics of near-surface sound propagation significantly affects their ability to detect low-frequency sounds. Additionally, a phenomenon known as the Lloyd mirror effect can attenuate or cancel the propagation of lower-frequency sounds generated near the surface. Lastly, acoustical shadowing of forward propagating sound is another reason why manatees (and whales) may not be able to hear the sound of large ships and boats. Therefore, manatees may have a poor ability to detect the sound of slow-moving boats, especially near the water surface.

Nowacek et al. (2004) verified that manatees do respond to approaching boats.

Although these responses vary with the individual manatee, within a typical response, a manatee increases swimming speed and moves toward or into deeper water. Manatees in deep water have more options for responding to approaching boats.

Therefore, three possible situations may have contributed to the collision of a manatee with a boat. The first one is that the manatee could not hear the approaching

5 boat. Second, although the manatee has heard the sounds of approaching boats, it does not have sufficient time to react and avoid being hit. The low-frequency sounds of many boats are omni directional and, therefore, by their nature, difficult to locate. Therefore, the third possibility is that the manatee is unable to localize the position of the approaching boat, causing it to move in harm’s way.

Contributions

Based on a review of the related literature, this dissertation constitutes the first effort to extend the range of manatee detection by using advanced signal processing techniques to extract manatee vocalizations that are buried in background noise.

Manatee vocalizations that were obtained from the recordings made by O’Shea

(1981-1984) are classified in ten different categories according to the frequency characteristics of manatee calls. Virtually all manatee vocalizations can be characterized by one of these ten categories. A library of 100 manatee calls is created (10 from each category) to evaluate the performance of FIR structure ALE (FIR-ALE) and FALE in terms of signal-to-noise ratio (SNR) with lower and upper bounds.

Simulations are performed to determine the optimal delay parameter for three sinusoids corrupted by white noise. Although the optimal value of the delay parameter for three sinusoids corrupted by white noise has not been investigated, the formula used to compute the optimal value is not derived in this dissertation because of the computational complexity. However, these simulations can be used as a guide to select the optimal delay parameter and as the basis for further work. Therefore, these simulations are not shown in the text body but are discussed in Appendix A.

The Finite Impulse Response (FIR) Adaptive Line Enhancer (ALE) and Feedback

Adaptive Line Enhancer (FALE) are implemented to reduce the background noise in

MATLABTM. A lower bound and an upper bound are proposed to evaluate the performance of FIR-ALE and FALE based on the established library of the manatee vocalizations in terms of SNR and their performance are compared with a bandpass filter as the baseline. A field test in land is performed to evaluate the performance of bandpass filter, FIR-ALE, and FALE on the acoustic superposition of background noise and manatee vocalizations. Two speakers are used to broadcast the manatee vocalizations and background noise, respectively. A microphone is used to measure the acoustic superposition of these two sources. However, real manatees and boat are not used in the field test due to practical constraints.

The computational requirements of the FIR-ALE and FALE algorithms are quantified in terms of the amount of multiplications and additions each algorithm needs.

The stability of FIR-ALE and FALE are discussed. The comparison between the convergence rate and tracking ability of FIR-ALE and FALE are also investigated. The advantages and disadvantages of the two algorithms are discussed in relation to a system that could potentially be constructed and used in the field.

The detection range for a prototypical system that implements background noise reduction techniques is estimated using the lower bound of these three algorithms and compared to the detection range of a system only using a bandpass filter. The simulation results show that the detection range is significantly improved. The improvement in detection distance is quantified, and the feasibility of an acoustically based manatee avoidance technology is also addressed.

Real time simulations in dSPACE are performed in a laboratory setting to further evaluate the performance of ALE in terms of correct detections, false detections, and

7 missed calls. The results show that the detection performance of the system is improved when the noise reduction algorithms are applied. The improved SNR of manatee vocalizations may be used to extend the range of detection of manatee vocalizations and reduce the false alarm and missing detection rate in their natural habitat.

Organization of the Dissertation

Within this dissertation, only an acoustic-based detection system is addressed. It is based on detecting the presence of manatees by using hydrophones that listen for manatee vocalizations. The frequency of manatee vocalizations, the source level of the vocalizations, the decay of the signal's strength with distance, and the amount of the ambient background noise will all affect the feasibility of an acoustic-based detection system. If the required hydrophone spacing is too small, the detection system will not be economically feasible. One way to increase the economic feasibility of such a system is to increase the minimum spacing of the hydrophones required by the system. One way to improve the detection capabilities of such a system and to increase the detection range is to artificially reduce the background noise. This is the primary focus of this dissertation.

The remainder of the dissertation is organized as described below.

In Chapter 2, other manatee detection approaches are reviewed. The advantages and disadvantages for these detection methods are also given. The vocalizations and behavior of manatees and two major background noise types, boat noise and snapping shrimp noise, are reviewed in the section of acoustic detection of manatee vocalizations.

A comparison between manatee calls and dolphin calls are made according to their frequency characteristics.

In Chapter 3, three different methods that may be used to reduce the background noise of manatee vocalizations are reviewed (i.e., Adaptive Noise Cancellation (ANC),

Blind Signal Separation (BSS), and Wavelet-based noise reduction). The BSS technique can be viewed as a generalization of the ANC. BSS avoids some limitations of an ANC system. The technique of Wavelet-based noise reduction is being investigated by Gur et al. (2005, 2006). However, within this dissertation, only ANC based on the Least Mean

Square (LMS) algorithm is investigated. A special adaptive noise canceller, Adaptive

Line Enhancer (ALE) that can be used to separate narrowband and broadband components from one signal is introduced for the first time in this dissertation.

In Chapter 4, the relevant theory of the adaptive filters is reviewed. It is shown that

ALE is suitable to reduce the background noise of manatee vocalizations. The theory of

FIR-ALE and IIR-ALE based on the LMS algorithm is developed. The literature of ALE including FIR-ALE and IIR-ALE is reviewed as well. Then, the theory of a constrained

IIR structure ALE (IIR-ALE) called Feedback Adaptive Line Enhancer (FALE) is presented.

In Chapter 5, in order to thoroughly test the performance of the FIR-ALE and

FALE algorithms, a library consisting of 100 manatee calls (ten categories) is created according to the frequency characteristics of manatee vocalizations. The manatee vocalizations in time domain and their spectrograms are shown in Appendix B.

In Chapter 6, the signal preprocessing before the ALE is applied is discussed first.

The literatures of the three important parameters of ALE are reviewed. The parameter selection of FIR-ALE and FALE is discussed for manatee problem in the section of parameter selection of ALE. The FIR-ALE and FALE based on LMS algorithm with a fixed step size is implemented in MATLABTM. The reason why the normalized LMS is not suitable to the manatee problem is discussed and other variable step size that provides

9 a large step size during manatee call periods and a small one for rest periods is difficult to implement. The performance of FIR-ALE and FALE for five manatee vocalizations from category 1000 in time domain is shown in the section of simulation results in time domain. In order to test them completely, the performance of FIR-ALE and FALE in terms of SNR based on the manatee vocalizations of the established library are estimated with a lower and an upper bound. Simulations show that the performance of FALE is worse than FIR-ALE for a majority of manatee calls when the SNR is low. The performance of bandpass filter, FIR-ALE, and FALE in time domain for two recordings of manatee vocalizations made by O’Shea (1981-1984) are also shown. A field test in land is performed to obtain the acoustic superposition of the background noise and manatee vocalizations. The conversion from spherical to mixed spreading is presented.

Finally, the simulation results are given.

In Chapter 7, a comparison between FIR-ALE and FALE is made from four aspects: computational complexity, stability, tracking ability, and convergence rate. The feedback of FALE increases the system gain; however, the feedback of FALE decreases the margin of stability, weakens the tracking ability, and slows the convergence rate. The advantage and disadvantage of FIR-ALE and FALE are presented for manatee problem.

In Chapter 8, the improvements of the detection range of the system enhanced by

FIR-ALE over bandpass filter, FALE over bandpass filter, and FALE over FIR-ALE, are estimated with the lower and upper bounds of their performance. The improved detection ranges of the system enhanced by the three algorithms are also estimated using the lower bound of their performance, respectively. The mean Sound Pressure Level (SPL) of boat noise (125 dB), manatee vocalizations (112 dB), and ambient noise (70, 80, 90, and 100

10 dB) after a bandpass filter is applied are used to estimate the detection range, respectively.

In Chapter 9, real time simulations using Simulink in a dSPACE system for testing the manatee recordings from O’Shea (1981-1984) are performed. The performance of

ALE is further evaluated in terms of correct detections, false detections, and missed calls.

The improved SNR of manatee vocalizations may be used to extend the range of detection of manatee vocalizations and reduce the false alarm and missing detection rate in their natural habitat.

Finally, in Chapter 10, conclusions are drawn concerning the feasibility of an acoustic-based manatee avoidance system. Several research topics deserved to be investigated based on my research are proposed. Although FIR-ALE and FALE algorithms work well in reducing the background noise of manatee vocalizations, two promising noise reduction methods, nonlinear adaptive filter and blind signal separation, are suggested.

CHAPTER 2 RESEARCH BACKGROUND AND REVIEW OF DETECTION METHODS

As discussed in Chapter 1, manatees have become endangered partly because of a growing number of fatal collisions with boats. Some researchers have investigated how to reduce the collisions with boats. Unfortunately, up to now, there is no effective method that can prevent manatees from being hit by boats. There are currently two different types of strategies to prevent the collisions. The first is a detection device that is used to alert boaters of the presence of manatees and enable boaters to avoid manatees without changing the behavior of the animals. The other strategy of manatee protection is technology designed to alert manatees of the presence of oncoming watercraft so that the animals can modify their behavior to avoid collisions. A high-frequency warning device designed to alert manatees to approaching boats is now being studied. Gerstein

(2004) proposed an acoustic warning system to alert manatees of approaching vessels.

However, critics claim that a manatee has to be struck by a boat before associating the sound with some danger. Additionally, unwanted sound is being injected into the environment that may affect other animals’ behavior. Therefore, only the first method is further considered in this dissertation.

In this chapter, three different methods of manatee detection are reviewed. The advantages and disadvantages of these three methods are analyzed. More attention is given to acoustic detection of manatee vocalizations. However, the background noise limits the detection range of the system. This dissertation focuses on the performance improvement for acoustic detection of manatee vocalizations using the technique of

11 12 background noise reduction. Therefore, a brief review of background noise reduction related to the manatee problem will be given in the next chapter.

Manatee Detection Methods

A growing number of fatal collisions with boats has lead to increased research into manatee avoidance technologies. Several methods to detect manatees have been proposed and include: 1) an above water infrared detection system (Keith, 2002); 2) an underwater active sonar based system (Bowles, 2002); and 3) a passive acoustic based detection system (Mann et. al., 2002; Herbert et al., 2002; Niezrecki et al., 2003). Each of these methods has their respective advantages and disadvantages.

Keith (2002) proposed the design of a boater manatee awareness system. An infrared detection system was designed to determine the number of manatees in a semi- enclosed area by detecting their exhalations in order to alert boaters to the number of animals in the area. He examined three technologies (infrared camera, night-vision scope, and video camera) and each of these technologies has their disadvantages. An infrared camera signal cannot penetrate water to image submerged objects such as manatees, and it is a very expensive approach. The images of a night-vision scope are of poor quality, and this quality is deleteriously impacted by the other ambient light sources.

The drawback of the third method is that images from video cameras do not penetrate the water well (unless the water is very clear), resulting in poor quality video images.

Bowles (2002) is developing a “Manatee Finder,” a sonar-based technology with the potential to reduce manatee-boat collisions. The initial goal is to design the sonar into a static platform that warns boaters of manatee presence. One of the key challenges of the technology is to distinguish the manatees from logs, other debris, fish and other marine mammals. Additionally, wave action in shallow water can cause false detection

13 due to a corrupted acoustic return signal. One of the advantages is that it can be active 24 hours a day, and it doesn't matter what the manatee is doing. The success of this project will depend in part on how well manatees’ bodies reflect sound waves back to the detector as well as the range at which they can be detected.

Mann et al. (2002) investigated passive acoustic detection of manatee sounds to alert boaters. Initial experimental results showed that background noise limit the ability to detect manatee calls to fairly short distance (on the order of 10 m). One method that can be used to increase the detection range is proposed in their paper. That method uses several hydrophones connected to one device to create an array that is capable of detecting manatees over a larger area, and which also could use beamforming techniques to improve the SNR. One advantage of that method is that it could also be used to localize the source and give guidance about the best way to avoid manatees. Herbert et al. (2002) developed a passive listening system that includes signal recognition software to detect manatee vocalizations. However, they did not provide a detailed description of their design and its performance in their report.

Niezrecki et al. (2003) implemented three detection algorithms including threshold method, harmonic content method, and autocorrelation method to analyze the noisy manatee call and made a comparison of the performance of the three methods. The autocorrelation method provided the best performance in terms of the number of manatee calls correctly identified, up to 96%. However, this method also resulted in a false alarm rate of ~16%.

Frisch and Haubold, (2003) suggested that the most promising results to date are from projects employing voice-recognition techniques to identify manatee vocalizations

14 and warn boaters of the presence of manatees. Sonar technology, much like that used in fish finders, is promising but has met with regulatory problems regarding permitting and remains to be tested, as has the manatee-alerting device.

Although the acoustic detection of manatee vocalizations are the most promising technique, it is believed that high levels of background noise, such as boat noise, snapping shrimp, and so on, significantly limits the effective distance of the detection device. Therefore, it will largely limit the widespread implementation of the device.

It is obvious that manatees can be detected further away from a hydrophone if the

SNR of the measured signal is improved. An efficient method to extend the detection range of an acoustic based system is to improve the SNR of a manatee call by reducing the background noise. If the detection range is increased, the quantity of required hardware needed for practical implementation will be reduced, making the system less expensive. At the same time, the detection accuracy will also be improved.

Acoustic Detection of Manatee Vocalizations

A conceptual sketch of how a manatee warning system may be implemented is shown in Figure 2-1. A hydrophone is used to measure the manatee vocalizations, and the measured signal is fed into the detection hardware to process. A decision strategy is applied to the processed signal and determines whether the manatee is present or not.

Only one hydrophone is used to measure the manatee vocalizations. Beamforming techniques are likely to be too costly and are not considered in this dissertation. The characteristic of the vocalizations and behavior of manatees are now reviewed.

Vocalizations and Behavior of Manatees

The animals of interest within this study are the West Indian Manatees or Florida

Manatees (Trichechus manatus). They are categorized within the order Sirenia which

15 includes the Dugong, Amazonian manatee (Trichechus inunguis), and African manatee

(Trichechus senegalensis). Schevill and Watkins (1965) were two of the first researchers to describe the vocalizations of the Florida manatee. They found that the manatees calls were not particularly loud and many of them were only 10 ~ 12 dB above background noise at distances of 3~4metres. In general, adult female sounds were lower in tone than those of adult males. A rise in amplitude of vocalizations occurred under conditions of distress, alarm, and annoyance (Steel, 1982). Nowacek (2003) also estimated the mean received sound pressure levels of the peak frequency to be approximately 100 dB (re 1

µPa). The received values were recorded with the hydrophone at approximately 20 m from a group of 50 manatees. By using the estimated position and the received sound pressure levels, the mean source level of the manatee was approximated to be 112 dB @

1m (Phillips et al., 2004).

Figure 2-1. Conceptual sketch of manatee warning system.

Steel (1982) was the first to perform a detailed categorization of manatee vocalizations. Nine different categories of adult vocalizations were established, such as squeal, squeak, rusty pumps, etc. Richard-Clark (1991) divided manatee calls into seven general categories: squeaks, squeal, lilts, whistles, chirps, peeps, and rusty pumps. She

16 compared the vocalization differences between the breeding population of manatees on the west and east coasts of Florida. The results indicate that manatees on the east coast vocalize at slightly higher frequencies than those on the west coast, implying that there may be a barrier between east and west coast breeding populations. O’Shea and the

United States Geological Survey (1981-1984) created one of the most extensive libraries of manatee recordings between 1981 and 1984.

Typical vocalizations of Florida manatee have a duration between 0.15 and 0.5 seconds. The fundamental frequencies of Florida manatee call are typically 2.5~5 kHz, but may be as low as 600 Hz. The highest frequency can be up to 16 kHz and recent research indicates that the higher order harmonics extend into the ultrasonic range. The differences between manatee calls generally correlate to the differences in animal age, gender, and size. The manatee squeak is composed of two or more frequencies that are not harmonically related and contain a greater amount of noise than the harmonic squeals

(Schevill and Watkins, 1965; Steel, 1982). The frequency spectrum of a typical manatee call, a harmonic squeal, is shown in Figure 2-2. The spectrogram of typical manatee vocalizations is shown in Figure 2-3. When harmonics are present, the second or third harmonic is often much more intense than the fundamental frequency (Nowacek et. al.,

2003). The magnitude of the higher harmonics decreases as the frequency increases.

Bengston and Fitzgerald (1985) studied the rate of calls made by manatees in 1985.

Apart from feeding, manatees vocalize approximately 1 to 5 times within a five-minute period. They observed that vocalization rates are dependant on a manatee’s behavior, with feeding and resting having lowest vocalization rates and mating and cavorting being the highest. They also suggested that if manatee vocalizations are used for

17 communicative and social purposes, then the vocalization rates might depend upon the number of manatees present. The rate of calls made appears to be low when they are feeding. However, they are not likely to be feeding within a protected channel.

Therefore, as long as a manatee-warning device remains active for a few minutes, this rate of vocalization should be adequate for detection and location of manatees.

110

100

30 Power Spectrum (dB) Spectrum Power

0 0 5 10 15 20 Frequency (kHz) Figure 2-2. Frequency spectrum of a typical manatee vocalization.

100 20 80

15 60

40 10

Frequency (kHz) Frequency 20

5 0

-20 0 0 1 2 3 4 5 6 7 8 9 Time (seconds) (dB) Figure 2-3. Spectrogram of typical manatee vocalizations.

Some researchers have investigated the vocalizations of the Amazonian manatee and found that the vocalizations were different from that of Florida manatee in some aspects. Sonoda and Takemura (1973) found that the Amazonian manatee swam more

18 actively than the West Indian Manatee and emitted underwater sounds continually. The duration range of Amazonian manatee vocalizations was originally measured to be from

0.15 to 0.22 second (Evans and Herald, 1970) and from 0.1 to 0.2 second (Sonoda and

Takemura, 1973). Later researchers’ finding increased this range to 0.05-0.5 second

(Sousa-Lima et al., 2002). Similarly, the fundamental frequency range has also been increased from 6-8 kHz (Evans and Herald, 1970) and 2-3 kHz (Sonoda and Takemura,

1973) to 1.07-8 kHz (Sousa-Lima et al., 2002). Evans and Herald (1970) found the majority of the sounds produced by the Amazonian manatee were louder than those observed for the Florida manatee. Sonoda and Takemura (1973) found that most of the calls of West Indian Manatee were frog-like calls of short duration consisting of several layers. The vocalization characteristics among different sexes and age classes of

Amazonian manatees were also investigated (Sousa-Lima et al., 2002).

Additionally several researchers have studied the vocalizations of the dugong. The vocalization of the dugong was also found to be similar to the manatee (Nair and Lal

Mohan, 1975; Anderson and Barclay, 1995). The results of this research may have application to all of the animals within order Sirenia.

Although a hydrophone can be used to measure the manatee vocalizations, manatee vocalizations are typically corrupted by a large amount background noise. The research shows that the background noise limits the ability of acoustic detection methods.

Major Background Noise

A manatee call signal may be corrupted by noise created by snapping shrimp, boats, rain, wind, fish, marine mammals, and wave motion. Although there are many sources of underwater noise, there are two primary sources of background noise that typically corrupt a manatee call. One is snapping shrimp noise and the other is boat

19 noise. The main part of the snap is extremely short with a peak followed by a number of oscillations as shown in Figure 2-4. The total duration is typically less than 10 ms (Au and Banks, 1998). The frequency spectrum of the snap is broadband with components up to 200 kHz. The difference between the peak and minimum of the spectrum of a typical snap is only 20 dB, which shows an extremely broad spectrum. The shape and magnitude of each snap is similar from click to click.

1.5

0.5

0 shrimp signal -0.5

-1

-1.5 0 1 2 3 4 5 6 7 8 9 10 Time (milliseconds)

Figure 2-4. Typical snapping shrimp noise in time domain.

Another important noise is boat noise. When a boat approaches the hydrophone location, the signal of the manatee call will be corrupted by the boat noise. The frequency spectrum of typical boat noise is shown in Figure 2-5. The main energy of boat noise is focused in the frequency range below 2 kHz. It is obvious that the boat noise is broadband noise compared to manatee calls. The noise other than snapping shrimp noise and boat noise are called “natural noise” in this dissertation (see Figure 2-

6).

120

100

40 Power Spectrum (dB) Spectrum Power

0 0 5 10 15 20 Frequency (kHz)

Figure 2-5. Frequency spectrum of typical boat noise

100

20 Power Spectrum (dB ref 1 uPa)

0 5 10 15 20 Frequency (kHz) Figure 2-6. Frequency spectrum of natural noise.

Comparison Between Manatee Calls and Dolphin Calls

Marine mammals vocalize in a variety of ways, each of them suited to a particular behavior or situation. Dolphin sounds can be classified into two broad categories: whistles that are narrow-band-frequency-modulated continuous tonal sounds and broadband sonar clicks that have durations between 50 and 200 µs (Evans, 1973). Most of the energy of clicks has spectral content larger than 20 kHz and the maximum frequency is up to 180 kHz. The duration and the spectrum of dolphin sounds make them

21 very different from manatee calls. Therefore, it should be fairly easy to distinguish the click of a dolphin and manatee call.

100 20

15 60

40 10

20 Frequency (kHz)

5 0

-20 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (seconds) Figure 2-7. Spectrogram of three typical dolphin whistles.

However, some dolphin “whistle” vocalizations were found to be very similar in base frequency to manatee “chirps”. The whistles usually vary in frequency with time

(Caldwell et al., 1990). However, its resonant structure is different from that of most manatee vocalizations. The spectrogram of a typical dolphin whistle is shown in Figure

2-7. The dolphin whistle has a frequency of 7-23 kHz. However, this is not the case for all whistles. Each individual dolphin also has a series of whistles distinct from any other member of the group called a signature whistle. This signature whistle distinguishes an individual, which provides a way for dolphins to recognize and bond with others. The lack of a resonance structure in dolphin whistles is utilized for discrimination from manatees and thus reduces false alarms that may be produced by dolphin activity.

Other Methods of Acoustic Detection

Several acoustic detection methods are discussed in the previous sections. Other methods of acoustic detection are discussed in this section, including: matched filtering,

Hidden Markov Model (HMM), Artificial Neural Network (ANN) algorithm, and spectrogram correlation.

Matched Filtering

A filter whose frequency response is designed to exactly match the frequency spectrum of the signal is called a matched filter. The frequency spectrum of the filter is an optimal method for detecting a known signal in white Gaussian noise (Van Trees,

1968). However, the matched filter is not necessarily the optimal solution when it is used to detect the signal that varies from one occurrence to the next, such as manatee calls.

Manatee calls are highly variable and include several categories of vocalizations, which are produced in a variety of unrelated circumstances (Steel, 1982). The background noise is also not white.

Although the sound structure of blue whales varies from one to another, a synthetic-kernel matched filtering proposed by Mellinger and Clark (1993) is used to detect blue whale sounds. In their paper, the synthetic-kernel matched filter simply performed cross-correlation. A threshold detection level is compared to the matched filter output to produce a series of discrete detection times. Stafford et al. (1998) used mean values for frequency and time characteristics from field-recorded blue whale calls to develop a simple matched filter for detecting the calls under noisy environment.

Hidden Markov Model (HMM)

HMM techniques have been widely used in speech recognition. The likelihood function is a discrete time data sequence that is produced by an underlying Markov chain.

The likelihood function is compared to the threshold to produce an indication when the sound has occurred. Rebiner and Juang (1986) have provided an excellent tutorial of the

HMM. The HMM techniques have also been used to classify underwater transient

23 signals (Huang and Rose, 1991; Weisburn et al., 1993; Dasgupta et al., 2001).

Experimental results have showed that the performance of HMM is better than that of matched filter but worse than that of spectrogram correlation (Mellinger and Clark,

2000).

Artificial Neural Networks (ANN)

ANN have been shown to be better than other methods at pattern classification when the input is noisy and the solution formulation is not well defined. ANN converge to a more accurate solution and embody more sophisticated responses. ANN also show good performance for handling time variations of transient signals. Although ANN exceed many other methods in detecting the sounds of a species of interest, they require a large training data set and the function of a trained network does not have a simple physical interpretation (Krieger et al., 1991; Potter et al., 1994; Erbe, 2000; Mellinger and

Clark, 2000).

Spectrogram Correlation

Spectrogram correlation is a method that uses the two dimensional synthetic kernel to cross correlate with a spectrogram of a recording. A recognition function, the probability at each point in time that the sound type is present, is produced to compare with a threshold to see whether the call is present. Spectrogram correlation is well suitable to recognize animal sounds consisting of tones and frequency sweeps, such as whales, manatees. Mellinger and Clark (1993, 2000) used spectrogram correlation to recognize transient low frequency whale sounds. They compared the performance of the spectrogram correlation to that of three other methods: matched filters, neural networks, and hidden Markov models. The experiments showed that, although the performance of

24 spectrogram correlation is little worse than that of neural networks, it requires a relatively small set of training sounds.

These four methods discussed above may be used to detect the manatees.

However, they will not be further discussed in this dissertation. The background noise cancellation for acoustic detection of manatee vocalizations will be mainly investigated in this dissertation.

CHAPTER 3 REVIEW OF BACKGROUND NOISE CANCELLATION

As stated in Chapter 2, a method to detect manatees via their vocalizations is being investigated. However, high-level background noise limits the detection range of the system. A method reducing the background noise of manatee vocalizations may extend the detection range. A brief review of noise reduction algorithms that may be effective for manatee problem is provided in this chapter. Apart from the standard low pass, high pass, and band pass filtering, there exist at least three advanced methods that could improve the SNR of manatee vocalizations by reducing background noise, which are

Adaptive Noise Cancellation (ANC), Blind Signal Separation (BSS), and Wavelet denoising. The technique of wavelet de-noising is currently being studied by Gur et al.

(2005, 2006). The technique of ANC is extensively investigated and implemented to reduce the background noise of manatee vocalizations in MATLABTM, Simulink, and dSPACE in this dissertation. One thing that needs to be clarified here is that the noise reduction is just adaptive noise cancellation and not performing active noise control.

That means no speaker is used to generate the control sources to reduce the background noise in the acoustic environment.

The simulation results (shown in later chapters) indicate that the technique of ANC is promising to improve the detection ability of the device by reducing background noise.

The technique of BSS may be investigated in the future. Therefore, more attention is given within the literature review on ANC. Conclusions are drawn on the appropriate approach for the manatee problem.

25 26

Adaptive Noise Cancellation (ANC)

In 1965, Kelly et al. (1965) conceived the idea to use adaptive transversal filters for echo cancellation while working at Bell Telephone Laboratories. A comprehensive review of ANC system was given by Kuo and Morgan (1996). They addressed some

ANC applications such as duct-acoustic noise, room acoustic noise, engine exhaust noise,

ANC headsets, fan noise, vehicle enclosures, aircraft cabins, and so on. All of these cancellation systems need a primary input and a reference input. It is expected that the reference input is only correlated with the background noise and not correlated with the desired signal in the primary input. The performance of ANC will be degraded if the reference input is correlated with the desired signal in the primary input or the reference input is not completely uncorrelated with the noise in the primary input or both.

Kuo and Morgan (1996) divided the architecture of ANC system into two structures: feedforward ANC and feedback ANC.

Feedforward ANC

dk() Σ + − ek( )

x()k yk()

Figure 3-1. Broadband feedforward ANC system.

A broadband feedforward ANC system is shown in Figure 3-1. The ANC system usually has a reference input and a primary input. For an active noise control system, the noise is measured by a reference sensor and processed by the ANC system to generate the control signal to drive a loudspeaker. The error measured by an error sensor is used to

27 update the coefficients of the adaptive filter. Essentially, an adaptive noise canceller is a dual-input, closed-loop adaptive feedback system.

Feedback ANC

In some cases, the reference signal is hard to obtain and can be easily estimated from the error signal and output of the adaptive filter. The feedback ANC algorithm can be used in this situation. The reference input of the feedback ANC derived from the adaptive filter and the error signal is a good estimate of the primary noise. Therefore, no additional microphone is required to pick up the reference noise, thus solving the crosstalk interference between microphones. Gan and Kuo (2003) presented the development and evaluation of an integrated active noise control communication headsets. They used an adaptive feedback ANC filter to reduce acoustic noise that corrupts the far-field signal inside the ear cups of headsets. However, in some cases, large noise level differences can make the algorithm unstable. The feedback ANC algorithm is widely used in some applications in which it is not possible to sense or internally generate a coherent reference signal (Tsuei et al., 2000; Kuo et al., 2003)

ANC for Underwater Acoustics

The underwater acoustic signals encountered are generally non-stationary and corrupted by unpredictable noise sources such as man-made noise, biological, and seismic noises. However, acoustic signal extraction and identification in an underwater environment can also be achieved by adaptive methods.

Gershman and Zverev (1994) performed signal detection and tracking of a weak moving signal in the presence of significant acoustic interference. The data from an experiment in the Baltic Sea was obtained by using an underwater horizontal receiving

28 array of 64 hydrophones. They implemented three adaptive beam forming algorithms for signal detection and tracking.

Catipovic et al. (1994) implemented ANC for underwater communications.

Acoustic communication with Autonomous Underwater Vehicles (AUV) can be corrupted by self-noise sources, such as on-board sonar systems, motor noise, and propeller blade-passing noise. Active emissions generated on-board the AUV provide the convenient reference signal correlated to the self-noise. Two methods of noise cancellation, a conventional ANC algorithm and multi-channel adaptive receiver algorithm, were proposed. The reference signal is easy to obtain in this application and the system can operate reliably in the SNR of -3 dB or worse.

Therrien et al. (1997) proposed a noise removal algorithm based on short-time

Wiener filtering. Noise statistics can be estimated in a region where only noise is assumed to be present, and the statistics of the received original signal can be estimated in the region where the signal and noise is present. The correlation of the desired signal is obtained by subtracting the correlation of the noise from that of the received noise- corrupted signal. A linear predictive filter was used to whiten the noise. An Inverse filter was also used to process the output data of Wiener filter.

Manatee vocalizations are measured by an underwater hydrophone and corrupted by high levels of background noise. Therefore, the ANC technique may also be used to reduce the background noise of manatee vocalizations. However, a reference input that is not correlated to the primary input is not available for manatee problem because the underwater background noise is nonstationary and different from place to place.

Therefore, ANC that does not need the reference input is required to solve this problem.

ANC without Reference Input

For both feedforward and feedback ANC, a reference signal that is not correlated with the desired signal in the primary input is required. A reference signal that is only correlated with the noise is not available for the manatee problem. We cannot estimate the signal-free noise by using a feedback algorithm. Therefore, we cannot use a hydrophone to get the (signal free) noise reference signal for the adaptive filter.

However, if we want to use an adaptive filter to reduce the background noise from the noisy manatee call, we must investigate another method to compensate for not having a noise reference input.

One problem that is similar to the manatee detection problem is the reduction of heart noise from lung sounds. Gnitecki (2003) proposed a RLS ANC filter to reduce heart noise when recording lung sounds. Likewise, it is also difficult to obtain the reference signal. The reference input for the Recursive Least Square (RLS) ANC filter was derived from a modified band pass filtered version of the original signal. Gnitecki discussed the shortcomings of the methods to obtain the reference signal used by other researchers (Lu et al., 1988; Kompis and Russi, 1992; Charleston and Azimi-Sadjadi,

1996; Hadjileontiadis and Panas, 1997; Yip and Zhang, 2001).

As stated in Chapter 2, the manatee vocalization can be assumed to be a narrowband signal compared to the background noise. This characteristic of manatee vocalizations makes Adaptive Line Enhancer (ALE) an excellent candidate to reduce the background noise. Widrow et al. (1975) were the first to propose ALE that can be used to detect and track narrowband signals in broadband noise. The simulations in Chapter 6 show that the ALE is a feasible method to obtain the reference signal and can be used to improve the ratio of the manatee call and background noise. A detailed theoretical

30 development of the ALE will be presented in Chapter 4. The structure of ALE is also an important factor determining its performance.

ANC Structures

The adaptive lattice predictor that consists of a number of cascaded stages makes the correlated reference signal uncorrelated (Haykin, 2002). The decorrelation of the signal at each stage allows the Least Mean Square (LMS) algorithms to converge much faster than the transversal filter and greatly reduces sensitivity to the eigenvalue spread of the reference signal. However, these advantages come at the expense of increased computational complexity. The RLS algorithm provides faster convergence and smaller steady-state error than the LMS algorithm at the expense of increased computational complexity as well. The sampling frequency of manatee vocalizations is as high as 48 kHz. The increased computational complexity needs a fast DSP processor, thus increasing the cost of the system.

A frequency domain ANC reduces computations by replacing the time-domain linear convolution with a multiplication in the frequency domain. However, larger delays between the input of the reference signal and the output of the secondary signal occur. A subband ANC algorithm was proposed due to the computational burden that wideband

ANC has, requiring hundreds of taps (Gilloire and Vetterli, 1988). However, the delay in the error feedback path due to the band pass filters reduces the maximum stable step size of the LMS algorithm, thus limiting the convergence rate.

For many situations in which undesirable noise is transmitted in several spatial dimensions, a multi-channel ANC system with multiple secondary sources and multiple error sensors is required to cancel the noise. This strategy not only improves the

31 performance of ANC but also localizes the position of sources. However, multiple sensors increase the cost of the system.

Although the LMS algorithm has some shortcomings, it is still popular in many applications due to its simplicity. Therefore, the ALE-based on an LMS algorithm is selected to reduce the background noise of manatee vocalizations. The technique of BSS may be another promising method to solve manatee problem and is reviewed briefly below.

Blind Signal Separation (BSS)

A filtering problem humans are familiar with is the cocktail party phenomenon.

We can focus on a speaker in the noisy environment of a cocktail party, despite the fact that the speech signal originating from that speaker is buried in undifferentiated background noise caused by other interfering conversations in the room. The technique of blind signal separation can separate N signals that have been mixed together in some unknown manner. More specifically, given N signals that have been mixed together in some unknown way and recorded by N sensors, the goal of blind signal separation is to recover the N original signals. The technique of blind signal separation is blind in the sense that it assumes that nothing is known about the mixing parameters. The key assumption is that the N source signals are mutually independent.

The blind signal separation problem can be viewed as a generalization of the ANC problem. In the blind signal separation algorithm, a reference signal that is only correlated with background noise component in the primary input is not required. Both the desired and interfering source signals of the ANC system are viewed as desired output signals. The leakage of the desired signal into the reference input of LMS algorithm limits the amount of noise reduction, which will be described in Chapter 4. The Blind

Signal Separation (BSS) approach can overcome this problem by adding a separation

filter h21 shown in Figure 3-2 to account for the leakage path. Therefore, BSS systems have a potential advantage over ANC systems in applications where leakage is a problem.

The investigation of the blind separation problem is often limited to the 2 by 2 case

by many researchers, and this case is shown in Figure 3-2. Two signals, s1 (k) and

s2 (k) , are mixed together in some unknown ways to form the received signals

x1 (k) and x2 (k) . After processing through the separation network, the output of the

network, sˆ1 (k) and sˆ2 (k) , are the estimation of the original signal s1 (k) and s2 (k) ,

where h11 , h12 , h21 , h22 are the relations that s1 (k) and s2 (k) are mixed together to form

x1 (k) and x2 (k) .

x1 ()k h11 s1 ()k

sˆ ()k h21 1

sˆ2 ()k

h12

s ()k x2 ()k 2 h 22 Figure 3-2. Illustration of blind signal separation.

Jutten and Herault (1991) proposed a recurrent neural network approach to separate scalar mixtures for the 2 by 2 case shown in Figure 3-2 (Jutten and Herault, 1991). The relation in Figure 3-3 can be written as

skˆˆ11122()= xk ()− wsk () (3.1)

skˆˆ22211()= xk ()− wsk () (3.2)

where ww12, 21 are the feedback parameters from sˆ2 (k) and sˆ1 (k) , respectively.

Solving these two equations, we get

x1122()kwxk− () skˆ1()= (3.3) 1− ww12 21

x2211()kwxk− () skˆ2 ()= (3.4) 1− ww12 21

sˆ1 ()k x1 ()k

w12

wh1121

sˆ ()k x2 ()k 2

Figure 3-3. Herault-Jutten method for blind signal separation.

Chan (1997) compared the performance of blind signal separation algorithm and that of ANC algorithm in the presence of signal leakage and found that the ANC system performed poorly when there was a significant amount of leakage. Gaeta et al. (1997) used the Herault-Jutten network to separate mixtures of simulated complex underwater signals in shallow water environment. They proposed a local whitening procedure that does not impact the separate signal output and preserves the signal characteristics. The use of IIR filters and the estimation of non-minimum phase filters can be investigated to improve the performance.

There is a certain amount of leakage between the primary input and the reference input obtained by delaying the primary input. This unavoidable leakage makes the performance of ALE algorithm an upper bound. Therefore, blind signal separation may provide better performance than ANC when used to reduce the background noise of manatee vocalizations. However, the technique of blind signal separation needs two or more hydrophones, thus increasing the cost of the system implementation. Meanwhile,

34 due to limited time and resources, the investigation of BSS will not be performed in this dissertation.

Wavelet-Based Noise Reduction

Transient signals are not well suited for standard spectral analysis methods due to the nonstationary behavior. In particular, Fourier-based methods are ideally suited to the extraction of narrow band signal whose duration exceeds or is at least on the order of the

Fourier analysis window length. Short Time Fourier Transform (STFT) with its non- varying window is not readily adaptable for capturing signal-specific characteristics.

While classical methods usually do not work in some cases, the recent use of multiresolution algorithms, such as adaptive wavelet transform and its dual, the cosine packet transforms, provide a promising alternative (Delory and Potter, 1998).

Another noise reduction method that may be used to reduce the background noise of manatee vocalizations is a method based on wavelets (Gue et al., 2005). In this approach, the noisy signal is expanded on an appropriate orthonormal basis that is made using some form of cost function (Seok and Bae, 1997). The coefficients of the expansion are ordered in terms of magnitude. A threshold value is used to separate the wavelet coefficients. It is assumed that a large-magnitude wavelet coefficient represents an important feature of the signal, and generally should not be altered, while a small- magnitude wavelet coefficient represents a noisy component of the signal, which should be attenuated or eliminated from the signal before reconstruction. The residual terms consist of the noisy part of the input signal and are treated as a new signal, which is in turn expanded and divided into its coherent and noisy components. This iteration process continues and the coherent portions from each expansion are combined to produce an estimate of the clean signal.

Learned et al. (1992) proposed the Wavelet Packet Transform (WPT) to detect and classify snapping shrimp and whale clicks in background noise. Wavelet packet based feature set provided excellent separation of class specific characteristics. Ravier and

Amblard (1996) proposed a transient detector based on Malvar wavelets. The proposed algorithm uses the adaptive Malvar wavelet transform to detect the transient acoustic signals in very low signal-to-noise ratio contexts.

Delory and Potter (1998) used the Wavelet Packet Transform (WPT) and the

Cosine Packet Transform (CPT) to extract a humpback whale vocalization from three types of noise: pink noise, snapping shrimp noise, and shipping noise. These two algorithms of signal extraction are efficient in environments where little is known on noise sources. They suggested that the adaptive algorithm may fail in such an environment.

Berger et al. (1994) also used wavelet denoising to restore old musical recordings of piano and vocal arrangements. They indicated that wavelet denoising was useful for removing noise from musical signals. However, it also created several undesirable artifacts in the restored signal. It appears that while wavelet denoising may offer an alternative method for noise reduction, it has several shortcomings that may limit its performance.

The technique of noise reduction based on wavelet is currently being studied by

Gur et al. (2005, 2006) to reduce the background noise of manatee vocalizations. The improvement of the wavelet algorithm is also being investigated. The simulation results showed that wavelet denoising is another promising method to reduce the background noise of manatee vocalizations.

Conclusions

Within this chapter, the literature of three methods to reduce background noise, adaptive noise cancellation, blind signal separation and wavelet based noise reduction, are reviewed briefly. The blind signal separation problem can be viewed as a generalization of the ANC problem. A reference signal that is only correlated with the background noise is not available for manatee problem. The manatee vocalizations are narrowband signals compared to the background noise, which will be discussed in detail later. The ALE algorithm that can detect the narrowband signal in broadband noise by using only a single input is more suitable to reduce the background noise of the manatee vocalizations. Although other methods may perform adequately, they will not be considered in the remainder of this dissertation. The next chapter provides a theoretical development for ALE.

CHAPTER 4 ADAPTIVE LINE ENHANCER (ALE)

In this chapter, an Adaptive Line Enhancer (ALE) is examined as a potential means of separating background noise from manatee vocalizations. As described in Chapter 3, many adaptive filtering techniques usually require a reference input and a primary input, thus violating the single-input requirement for manatee detection system implementation.

The ALE is an implementation of adaptive filtering that has applications in detecting and tracking narrowband signals in broadband noise and only needs a single input. It is known that delayed broadband signal components in the reference input will become uncorrelated with the original broadband signal in the primary input. The narrowband components will remain correlated with each other because of their periodic nature.

Therefore, the reference signal of ALE can be obtained by delaying the primary input signal. The manatee vocalization is a narrowband signal compared to the broadband background noise. Therefore, as discussed in Chapter 3, the ALE based on the LMS algorithm is suitable to reduce the background noise of the manatee vocalizations.

This chapter begins with a brief review of the Wiener filter and the LMS algorithm.

Then, the theory of FIR-ALE and IIR-ALE are developed. Next, a brief literature review of FIR-ALE and IIR-ALE is given. Finally, the theory of a constrained IIR-ALE, called

Feedback ALE (FALE), is also developed.

General Adaptive Filter

Widrow et al. (1975) were the first to describe the concept of ANC and created a method of estimating signals corrupted by additive noise or interference. The primary

37 38 input contains the corrupted signal (signal plus noise), and the reference input contains noise correlated in some unknown way with the noise in the primary input. The output of the adaptive filter is adjusted to cancel the noise in the primary input, resulting in only the signal for an ideal case. In active noise control system, the residual noise measured by an error microphone is used to update the coefficients of the adaptive filter to minimize the residual noise.

Wiener Filter

The Wiener solution shows that the noise in the primary input can be essentially reduced without signal distortion when the reference input is not corrupted by the signal

(Widrow et al., 1975). A block diagram of the Wiener filter is shown in Figure 4-1,

where x(k ) represents the reference input, Aaa= [01 " aL− 1 ] and represents the weights of the Wiener filter, L represents the order (weight taps) of the Wiener filter, yk() represents the primary input, and ykˆ() represents the output of Wiener filter, which is an estimate of yk ( ) . The error, ek ( ) , is the difference between the primary input and output of the Wiener filter and can be expressed as

ek()=− yk () ykˆ () L−1 * (4.1) =−yk ( )∑ axkn ( − n ) n = 0, 1, 2, " , L − 1 n=0 where the asterisk represents the operation of complex conjugate under the assumption that the weight coefficients are complex valued. The Wiener-Hopf equation is given by

(Haykin, 2002)

RxxAP opt= xy (4.2)

−1 After multiply both sides of Eq. (4.2) by Rxx , the Wiener solution is given by

−1 ARPopt= xx xy (4.3)

where Aopt represents the coefficients of the minimum Mean Square Error (MSE) Wiener

filter. Pxy is the cross-correlation vector between the reference input and the primary input and given by

PEXkykxy = [()()] (4.4) where

X( k )= [ xk ( ), xk(−−+ 1), " , xk( L 1)] (4.5)

Rxx is the autocorrelation matrix of the reference input and given by

⎡⎤rrrrLxx(0) xx (1) xx (2)" xx (− 1) ⎢⎥rrrrL(1) (0) (1)" (− 2) ⎢⎥xx xx xx xx

Rrxx= ⎢⎥ xx (2) %%%# (4.6) ⎢⎥ ⎢⎥#%%%# ⎢⎥ ⎣⎦rLxx(1)(2)−− rL xx"" r xx (0) where

rjxx ()= Exkxkj [()(− )] (4.7)

y()k + xk() yˆ()k − ek() A Σ

Figure 4-1. Block diagram of Wiener filter.

Although the Wiener solution gives the optimal filter, the computation of the optimum weights requires knowledge of two quantities: (1) the inversion of the autocorrelation matrix of the reference input and (2) the cross-correlation between the reference input and the primary input. Therefore, it is time-consuming to compute the optimal weights using the Wiener solution. The LMS algorithm is often used due to its

40 simplicity. It does not require measurement of the pertinent correlation functions, nor does it require matrix inversion.

Least Mean Square (LMS)

A simplified block diagram of ANC based on the LMS algorithm is shown in

Figure 4-2, where x (k ) is the reference input, yk ( ) is the primary input, and ek ( ) is the error used as a feedback to update the weight coefficients represented by Ak ( ) .

Therefore, the error signal is expressed as Eq. (4.8)

ek()= yk ()− ykˆ () (4.8) =−yk () AT () kXk ()

T T where Ak()= [ akak01 () () " aL− 1 ()] k, X ( k )=− [ xk ( ) xk ( 1) " xk ( −+ L 1)] , and

L is the order of the adaptive filter. ""T represents the operation of transpose under the assumption that the weight coefficients are real valued. The cost function based on MSE is given by

Jk()= Eek [()]2 (4.9)

In LMS algorithm, the instantaneous squared error shown in Eq.(4.10) is used as the estimate of the expectation value.

Jkˆ()= ek ()2 (4.10)

The steepest descent algorithm is used to update the weight vector in a negative gradient direction with step size µ . The weight update of the adaptive filter is given by

µ Ak(1)()+= Ak −∇ Jˆ () k (4.11) 2 where ∇Jkˆ() is an instantaneous estimate of the MSE gradient at time k and expressed as

∇≈∇=∇=∇Jkˆ() Jk () e2 () k 2[ ek ()] ek () (4.12)

Differentiating ek( ) in Eq. (4.8) with respect to Ak ( ) , then

∇ek()=− X () k (4.13)

Therefore, the gradient estimate becomes

∇=−Jkˆ() 2 Xkek ()() (4.14)

Substituting Eq. (4.14) into Eq. (4.11), the weight update of LMS algorithm is given by

Ak(1)()+ =+ Akµ X()() kek (4.15)

yk() + ek() Σ − x()k ykˆ() Az()

LMS

Figure 4-2. Simplified block diagram of adaptive noise canceller based on LMS algorithm.

If the desired signal in primary input is zero and the reference input is completely correlated with the noise part of the primary input, the adaptive filter will drive the output ek() to zero. However, the LMS algorithm suffers some limitations, including slow convergence rate, large weight vector noise, etc.

Limitations of the LMS Algorithm and ANC System

One of the main limitations of the LMS algorithm is its potentially slow convergence rate. An important factor in determining the convergence rate of the LMS algorithm is the eigenvalue spread of the autocorrelation matrix of the reference input.

The maximum eigenvalue of the correlation matrix determines the largest step size by

(Haykin, 2002)

2 0 <<µ (4.16) λmax

where µ is the step size of the adaptive filter and λmax is the maximum eigenvalue of the autocorrelation matrix of the reference input. For a given value of the step size, the convergence rate of LMS algorithm is determined by the mode corresponding to the smallest eigenvalue. If a transversal filter is used, the rate of convergence can be improved by using an adjustable-step-size LMS algorithm (Harris et al., 1986; Evan et al., 1993; Kim and Poularikas, 2002; Wang, et al., 2003), Newton algorithm (Widrow and

Stearns, 1985), Kalman algorithm (Haykin, 2002), or RLS algorithm at the expense of the complex computation. Other approaches condition the reference signal by employing different filter structures such as the lattice filter, sub-band filter (Morgan and Thi, 1995), or orthogonal transform (Kuo and Morgan, 1996).

While a large value of step size implies a faster rate of convergence, it also causes a larger misadjustment (Haykin, 2002). The misadjustment is formally defined as

J ()∞ M = ex (4.17) Jmin

where J ex (∞) represents the steady state value of the excess MSE and J min represents the minimum MSE. Therefore, there is an inevitable tradeoff between the rate of convergence and the amount of noise reduction that an LMS-based ANC can achieve.

The ANC system depicted in Figure 3-1 represents an ideal case. A more realistic scenario of the ANC system is shown in Figure 4-3. Leakage of the desired signal into the reference input places an upper bound on the amount of noise cancellation that can be achieved. At the same time, the leakage also causes some distortion of the noise-reduced

signal at the ANC output. The upper bound of SNR at the ANC output, max{SNRo }, is given by (Widrow et al., 1975)

1 max{SNRo } ≤ (4.18) SNRre

where SNRre represents the SNR of the reference input. Widrow et al. also derived an expression to estimate the signal distortion D at the ANC output, which is given by

SNR D ≅ re (4.19) SNRpr

where SNR pr represents the SNR of the primary input. The effect of other noise shown in Figure 4-3 on the performance of the filter can be found in the paper by Widrow et al.

(1975).

dk()

ek()

x()k yk()

Figure 4-3. Block diagram of an ANC system under realistic conditions.

Although the LMS algorithm has the limitation of slow convergence rate, the simple computation of LMS still makes it very popular in many applications. Widrow et al. proposed the ALE algorithm based on the Widrow-Hoff LMS algorithm (Widrow et al., 1975). The ALE based on the LMS algorithm is used to reduce the background noise of manatee vocalizations in this dissertation.

The structure of ALE can be classified into two main categories: FIR structure ALE

(FIR-ALE) and IIR structure ALE (IIR-ALE). These are described below.

Theory of FIR-ALE

The block diagram of FIR-ALE is shown in Figure 4-4. The observed signalx(k ) is assumed to be of the form

x()ksknk= ()+ () (4.20) where s(k) is the sum of a number of narrowband components and n(k ) is assumed to be a zero-mean white Gaussian noise with power v 2 , which is independent of s(k) . The portion shown in the dotted box represents a ∆ -step predictor.

Σ ek() x()k

z−∆ z−1 z−1 x′()k

a 1 aL−1

sˆ()k Σ Σ

Figure 4-4. Block diagram of FIR-ALE.

The reference input, x′()k , is obtained by delaying the observed signal and given by

xk′()()()()= xk−∆ = sk −∆ + nk −∆ (4.21)

The estimate of s(k) , which is skˆ(), is formed as

LL−−11 ˆ ′ sk()=−=−∆−∑∑ aii () kx ( k i ) a ()( kxk i ) ii==00 (4.22)

=−∆+−∆−++−∆−+a01 ( kxk ) ( ) a ( kxk ) ( 1)" aL− 1 ( kxk ) ( L 1)

where the coefficients of adaptive filter, {ai }, are updated by the error e(k) so as to minimize the cost function given by

JExksk=−[(()ˆ ())]2 (4.23)

The error sequence is fed back to adjust the weights of the adaptive filter according to the

Widrow-Hoff algorithm (Zeidler et al., 1978), which is given by

akii (+= 1) ak ( ) +µ ekxki ( ) ( −−∆ ) i = 0, 1, " , L − 1 (4.24) where µ is a constant. If the cancellation is ideal, the adaptive filter will cause skˆ() to be a prediction of the current value of s(k ) , and the error will be the broadband noise only.

The delay must be of sufficient length to cause the broadband signal components in the reference input to become de-correlated from those in the primary input. The harmonic components will remain correlated with each other because of their periodic nature. Simulations in Chapter 6 show that the ALE is a feasible method to obtain the reference signal of adaptive filter and can be used to improve SNR of the manatee vocalizations. The adaptive filter forms a transfer function equivalent to that of a narrowband filter centered at the frequency of the sinusoidal components. The noise component of the delayed reference input is rejected because it is uncorrelated with any components of the primary input. The phase difference between the sinusoid of reference input and primary input is adjusted by the adaptive filter so that they cancel each other at the summation.

The FIR-ALE is widely used because of its stability. However, it is computationally intensive when good accuracy is required because a large filter order is required. From the instantaneous transfer function of the adaptive filter, the FIR-ALE does not give the optimal estimate of the manatee call (see Chapter 6). A larger order can narrow the filter pass band about the center frequency, thus improving the estimate of signal amplitude for a given SNR of the input (Rickard and Zeidler, 1979). However, the

46 order of the ALE cannot be chosen to be too large because of the unavoidable misadjustment, which affects the minimum error the adaptive filter can achieve. The misadjustment will increase with the increase of the order of the adaptive filter. The theoretical expression for misadjustment is given by Widrow et al. (1976)

ML= µ φxx (0) (4.25) where µ represents the step size of the adaptive filter, L is the order of the adaptive

filter, and φ xx is the autocorrelation function of the input of ALE, and given by

φxx ()j = Exkxk [()(+ j )] (4.26)

Although the misadjustment level can be reduced by decreasing the step size µ , it will lengthen the convergence time of the adaptive filter. Sometimes a relatively large step size should be chosen to track a nonstationary signal. The SNR of the narrowband output is limited by the unavoidable misadjustment noise of ALE. From the Eq. (4.25), it is easy to see that the order cannot be too large in order to avoid large misadjustment.

Therefore, there exists a tradeoff between the misadjustment of the weight vectors and the estimate accuracy of the model. Furthermore, a filter with a large order requires a longer computation time.

Therefore, the FIR structure is sub-optimal for modeling the underlying process.

The IIR structure is proposed because of the computational advantage and their potentially better performance (Haykin, 2002). The transfer function that IIR structure achieves can provide an optimal solution.

Theory of IIR-ALE

The IIR-ALE is proposed as an alternative to the FIR-ALE when more weight taps are required. A block diagram of IIR-ALE is shown in Figure 4-5. The structure of an

IIR filter is identical to that of the Autoregressive Moving Average (ARMA) model, which is defined by

MN ′ yk()= ∑∑ bii () kx ( k−+ i ) a ()( nyk − i ) (4.27) ii==01

where ani ( ) and bni ( ) are the adjustable coefficients of the model. The transfer function of the ARMA model can be expressed as

Yz() Bz () Hz()== (4.28) X ′()zAz 1− ()

x()k + ek() Σ − x′()k + yk() z−∆ Bz() Σ + A()z

Figure 4-5. Block diagram of IIR-ALE.

The poles of the IIR-ALE are added into the system due to feedback. The IIR structure can improve the frequency response and provide more accurate estimates in system identification applications than FIR filters using the same number of filter coefficients. However, the output of the adaptive filter is no longer simply a linear function of the filter coefficients due to its feedback. Consequently, the error surface, a plot of the mean square error versus the coefficients of the adaptive filter, is not quadratic and may have local minima (Stearns, 1981). Therefore, the existing gradient search methods may not always find the global minimum, which reduces the performance of

IIR-ALE.

Another problem caused by the poles is the stability of the system. The IIR filter is no longer unconditionally Bounded-Input Bounded-Output (BIBO) stable due to the

48 feedback (Haykin, 2002). Real time stability monitoring may be needed and increases the computational burden. Therefore, the computation time of IIR-ALE is reduced at the expense of the instability problem and slow convergence rate.

Review of ALE

FIR Structure ALE

Widrow et al. were the first to propose that ALE can be used to detect a narrowband signal in broadband noise (Widrow et al., 1975). McCool and Widrow

(1976) suggested that ALE can be used to detect sinusoidal signals in correlated or colored noise in which a relatively large value of the delay parameter is needed to ensure decorrelation between the noise component in reference input and the primary input.

Zeidler et al. (1978) analyzed the steady state behavior of ALE for a stationary input consisting of multiple sinusoids in white noise. The Wiener-Hoff matrix equation describing the steady state impulse response of ALE may be transformed into a set of 2N coupled linear equations, where N is the number of sinusoids. This set of equations will become increasingly decoupled as the order of adaptive filter becomes large.

Reddy et al. (1981) showed that there exists an optimum value of the decorrelation parameter, ∆, for a single sinusoid. A lattice form implementation of the ALE was investigated because of its rapidly convergent algorithm in their paper. They compared the performance of the LMS algorithm and the lattice algorithm under the same iterations and found that the LMS algorithm performs worse than the lattice algorithm because of its slow convergence rate. The LMS algorithm requires many more iterations to reach the same performance as the lattice algorithm. The experiments also showed that the performance of the lattice-form ALE with on-line computation is comparable to the off- line maximum entropy method.

Egardt et al. (1983) derived the optimal choices of ∆ for two sinusoids when the

SNR of the input is high. Gupa (1984, 1985) and Yoganandam et al. (1988) derived the optimum value of ∆ for arbitrary SNR in the case of single sinusoid and two sinusoids in broadband noise, respectively. The optimal delay parameter of the ALE will be discussed in detail in the next section.

Rickard and Zeidler (1979) analyzed the second order output statistics of ALE.

They suggested that the ALE output r(k ) can be decomposed into a Wiener filter component and a misadjustment filter component when excited by the input x(k ) . The

relationship between SNRin and gain G is shown in Figure 4-6. The ALE gain G (in dB) defined by

GSNRSNR=10log10 oin / (4.29) is low when the SNR of the input is small or large and it is high when medium, where

SNRo represents the SNR at the output of ALE and SNRin represents the SNR of the

ALE input.

Gain G (dB) Gain -5

-10

-15

-20

-25 -50 -40 -30 -20 -10 0 10 SNR (dB) in Figure 4-6. The relationship between the SNR of input and the gain of ALE.

Anderson (1980) showed the effect of the input signal properties (bandwidth and

SNR) and ALE parameters (order, step size, and delay) on the performance of the ALE separating the narrowband signals from white noise. The results showed that the delay should be minimized to prevent significant signal decorrelation and the filter order should be sufficiently short to avoid unnecessary misadjustment. He also suggested that the optimal order of the ALE should be less than the inverse of the damping coefficient of the autocorrelation of the finite bandwidth signals. However, these results are obtained from the stationary data and may not be applicable to nonstationary signals.

Albert et al. (1991) compared the detection and tracking performance of ALE implemented with the traditional LMS transversal and the RLS Lattice algorithm. The results showed that the RLS Lattice exhibited about 3 dB better than LMS algorithm but only for longer filters and higher sweep rates. However, the computation time is greatly increased.

Dwyer (1991) suggested that propagating underwater signal are sometimes corrupted by multiplicative noise that decorrelates the sinusoid, spreads its power spectrum, and acts as an additional corrupting noise. Ghogho et al. (1998) studied the behavior of the ALE with the LMS algorithm when used to enhance the sinusoids corrupted by both colored multiplicative and white additive noise and demonstrated the capability of the ALE to reduce such noise.

IIR Structure ALE

The IIR structure adaptive filter is not widely used largely because of the lack of robustness. Up to now, many methods have been proposed to solve this problem, such as real-time stability monitoring (Shynk, 1989), Hyperstable Adaptive Recursive Filtering

(HARF) (Larimore et al., 1980, Johnson et al., 1981), equation error approach (Mendel,

1973; Gardner, 1981), and so on. However, all of these methods pose other disadvantages. For example, the stability monitoring and HARF require significant additional computation, while the equation error approach can lead to biased estimates of the coefficients.

Some IIR structures of the ALE with constrained coefficients were also proposed to enjoy a computational advantage and their potentially better performance. Thompson

(1978) first proposed a constrained recursive adaptive notch filter in which the relationship between the feedforward coefficients and the feedback coefficients is given by

i abii= ρ ρ <1 (4.30)

where ai and bi are the feedback and feedforward coefficients of the adaptive filter.

This constraint makes the poles of the IIR system stay on approximately the same radii as the zeros, respectively.

The constraint proposed by David et al. (1983) is to fix the radius of the adaptive poles and allow the poles to move on a fixed circle within the unit circle. Hush et al.

(1986) continued working on this approach and pointed out that the performance surface becomes less uniform and extremely flat in areas away from the minimum as the pole radius approaches 1, or as the SNR of the input gets smaller. This suggests that a pure gradient search technique may be somewhat inefficient and the adaptation time of IIR-

ALE may be longer than that of FIR-ALE.

Nehorai (1985) proposed a special constraint model of IIR with a minimum number of coefficients required for a notch filter. The mirror symmetric constraint of the numerator of the notch filter places the zeros of the adaptive filter on the unit circle. The

52 filter denominators of the general form Az()ρ −1 maintains the poles on the same radial lines as the zeros, but slightly displaced towards the origin, where ρ is a positive real number close to but smaller than 1. He claimed that the advantages of this notch filter include computational efficiency, stability, more accurate results, numerical robustness, faster convergence, and better controllability on the performance when compared to previous schemes. However, the Gauss-Newton type algorithms used by this approach are still computationally complex and quite sensitive to initial conditions.

Kwan and Martin (1989) proposed a constrained adaptive IIR filter that consists of a cascade of biquadratic notch sections to track multiple sinusoids. Constantinides et al.

(1992) proposed an ARMA structure based on classical Laguerre orthogonal functions.

Linear adaptation makes the ARMA structure avoid instability problems.

Feedback Adaptive Line Enhancer (FALE)

Another constrained IIR adaptive filter, the Feedback Adaptive Line Enhancer

(FALE), was proposed by Glover and Chang (1989), which is a modified version of the well-known ALE. A block diagram of FALE is shown in Figure 4-7. From this figure, the reference input, x′ (k ) , is the delayed version of the signal that is weighted average of the primary input x (k ) and the narrowband output skˆ(). The relationship is given by

xk′()= β skˆ (−∆ ) + (1 −β )( xk −∆ ) (4.31) where β represents the feedback constant. The enhanced sinusoid signal from narrowband output is added to the reference input, which increases the correlation of the sinusoid signal in the reference input with that in primary input. As the narrowband output is refiltered, the noise component is progressively reduced. The narrowband output, when initially fed back, consists of sinusoids signal that matched in phase to the

53 sinusoids in primary input, but smaller in amplitude and corrupted by residue noise.

Clearly, the FALE becomes FIR-ALE when β = 0 . There exists a choice of β that makes the FALE superior to FIR-ALE. Simulations performed by Glover and Chang show that the “optimum” value of β varies from 0.4 for the high SNR case to somewhat less than 0.9 for lower SNR case. For values less than 0.4, there is no clear advantage to the FALE. For values larger than 0.9, the estimation error is increased by the adaptation oscillations due to the feedback (Glover and Chang, 1989).

x()ksknk=+ () () ek() ∑

1− β

x′()k sˆ()k ∑ z−∆

Figure 4-7. Block Diagram of Feedback Adaptive Line Enhancer (FALE).

If P and Q are the feedforward and feedback components of the IIR filter, the

FALE has a relationship given by

PC= (1− β ) (4.32) QC= β where C represents the transfer function between the primary input and narrowband output of the FIR-ALE. Therefore, FALE is actually a constrained IIR adaptive filter.

The transfer function between the primary input and the narrowband output of FALE,

Hz(), is given by

Szˆ() (1− β ) z−∆ Fz () Hz()== (4.33) X ()zzFz 1− β −∆ ()

L−1 −k where Fz()= ∑ azk . The performance of FALE will be investigated in the next k=0 chapter, including an analysis of its computational complexity, convergence rate, tracking ability, and stability.

Chang (1993) compared the minimal parameter adaptive notch filter (MANF) proposed by Nehorai (1985) with the FALE based on the complexity of the algorithm and its performance enhancement. Although the MANF provides very narrow notches for the steady state input when the SNR of the input is high or moderate, the advantage brought by the constraint is valid only for the exact-order case. This adaptive notch filter is prone to divergence and gives incorrect notches for multiple sinusoid cases when the SNR of the input is low. On the contrary, the FALE works well in the low SNR, and the prior information about the number of sinusoids is not needed.

Marshall (1994) showed in his dissertation that the FALE algorithm can be interpreted as FIR-ALE whose reference input is the delayed version of primary input filter by a time-varying autoregressive filter formed from the weights of the FIR filter component.

CHAPTER 5 ESTABLISHMENT OF THE MANATEE LIBRARY

O’Shea and the United States Geological Survey created one of the most extensive libraries of manatee recordings between 1981 and 1984 (O’Shea, 1981-1984). These recordings are used to quantify the performance of the FIR-ALE and FALE algorithms in this dissertation. In order to completely evaluate the performance of FIR-ALE and FALE with numerous manatee vocalizations, a library containing 100 manatee vocalizations is established which attempts to cover all possible frequency characteristics of manatee vocalizations. Manatee vocalizations and background noise are numerically superposed in the simulations to evaluate the performance of the algorithms with different SNR of manatee vocalizations. The simulation results for numerical and acoustic superposition are shown in Chapter 6.

The theories of FIR-ALE and FALE have been discussed in Chapter 4. In order to test these two algorithms with real recordings, a library of the manatee calls is established. The categories of calls are differentiated by vocalizations that include clear or unclear harmonic frequency content, the number of dominant frequencies, and frequency variability within a single call. Each criterion has two or three different cases.

The library consists of 10 different categories that include a total of 100 different manatee calls. Each category contains ten calls that were obtained from the extensive library of recordings created by O’Shea. The ten different categories can cover all possible frequency characteristics of manatee vocalizations. Therefore, ten categories were sufficient to represent all of the different types of vocalizations. Therefore, a total of 100

55 56 manatee vocalizations are used to evaluate the performance of these three algorithms, i.e., band pass filter, FIR-ALE, and FALE.

It is important to point out that categorization is performed purely from a signal detection perspective. No attempt is made to infer what the significance of each category indicates in terms of manatee behavior. The procedure of classifying manatee calls is shown in Figure 5-1 (Yan et al., 2006). The first level of categorization discriminates a vocalization that either does or does not have some discernable harmonic content in which the dominant frequencies are at least 20 dB larger than the neighborhood frequencies. Likewise, if the powers of several frequencies of an individual manatee call are at least 20 dB larger than their neighborhood harmonic frequencies and the difference between them is less than 20 dB, all of these frequencies of the manatee call can be called dominant frequencies. Most manatee vocalizations do have harmonic structure. For the calls that do possess harmonics, a further subdivision is to identify calls that either have one, two (or three), or more than three dominant harmonics (where N refers to the # of harmonics present). The next level of categorization is to identify if the calls have a dominant frequency change. A frequency change is defined as a frequency shift in excess of 10 percent. These types of vocalizations can be used to test the frequency tracking ability of these two ALE algorithms. For those calls that do have a dominant frequency change, the last level of decomposition categorizes the frequency change as being continuous or discrete. The discrete frequency change is defined as a frequency shift in excess of 10 percent within a duration of 10 milliseconds.

No Yes

N =1 Nor= 2 3 N > 3

No Yes

1, 2, " , N Figure 5-1. The procedure of classifying manatee calls.

In order to discriminate between categories, a labeling system is adopted. The codes 0, 1, and 2, are used to represent different categories, and each manatee vocalization is categorized by a four digit number. For example, a manatee call with code 1111 represents that it has clear harmonic frequency content, the number of dominant frequencies is two or three, and the dominant frequency changes discretely with time. The ten different possible categories in the flow chart are represented within the library by ten different manatee calls that all have the same characteristics. For a

58 particular category, the following characteristics may be different from one call to the next: (1) the location of the dominant frequency; (2) the shape of the envelope of each manatee vocalizations in the time domain; (3) the power distribution of the harmonics; and (4) the overall power of the manatee call.

In some manatee calls, no distinct harmonic frequencies occur, but these calls can still be regarded as narrow band signals when compared with the background noise. The narrower the bandwidth of the manatee calls and the wider the background noise, the better the performance of the ALE (Yan et al., 2005). Therefore, for the manatee calls without distinct harmonic frequencies, the performance of the ALE may degrade to some degree. Although the number of dominant frequencies of the manatee call may be one, two, three or more, the energy of most manatee calls is dominated by one or two harmonics.

In order to show these manatee vocalizations clearly, the manatee vocalizations in time domain and their spectrogram are shown in Appendix B.

CHAPTER 6 SIMULATION RESULTS AND ANALYSES

The theories of FIR-ALE and FALE have been developed in Chapter 4. The database for testing the performance of FIR-ALE and FALE with real recordings is established in Chapter 5. In this chapter the performance of these two algorithms is evaluated with real recordings of manatee vocalizations.

This chapter is organized as follows. Signal preprocessing before FIR-ALE or

FALE is applied is discussed first. Then, the parameters, including order, delay, and step size, are selected carefully. The simulation results in the time domain and in terms of

SNR are shown in the next two sections, respectively. Finally, a field test is performed in land to obtain the acoustic superposition of manatee vocalizations and boat noise. The simulation results on acoustic superposition are also shown and discussed.

Signal Preprocessing

Since the fundamental frequency of manatee calls typically lies between 2 kHz and

5 kHz, a band pass filter (tenth-order Butterworth IIR filter) is used as baseline system to compare and evaluate the performance of the FIR-ALE and FALE. The pass band of the filter is given by

f12< ff< (6.1)

where f1 = 1.2 kHz and f2 = 20 kHz. The band pass filter is also used to preprocess the data before applying the adaptive filter. This greatly reduces the energy of noise at low frequencies that may degrade the performance of the ALE. In order to reduce the noise

59 60

with low frequencies, the value of f1 cannot be set too small. Since the highest

frequency of the manatee calls is typically less than 20 kHz, the value of f2 is set to 20 kHz. Experience has shown that a significant portion of the low frequency noise can be reduced without significantly affecting a manatee call by preprocessing the signal with a bandpass filter (Yan et al., 2005).

The fundamental frequency of some manatee calls may be as low as 600 Hz and the manatee calls without harmonics are generally of higher frequency, around 4 or 5 kHz

(Schevill and Watkins, 1965). However, the manatee calls with a fundamental frequency around 600 Hz are believed to be sounds generated when feeding (Steel, 1982), and manatees are not likely to be feeding in a channel.

Parameter Selection of ALE

Review of Delay Parameter

The delay parameter, ∆ , should be properly selected to reject the broadband component from the narrowband output of the LMS filter yet keeps the narrowband component highly correlated. Treichler (1977) suggested that the autocorrelation

function of noise with the delay of ∆ , rn (∆ ) , must be essentially zero for lags of ∆ or greater. Thus

rn ()∆ ≅ 0 (6.2)

−4 For example, it might be arbitrarily defined as 10 ⋅ rn (0 ) . The value of ∆ needed to exclude a signal with bandwidth B is given by

α ∆≥ (6.3) 2BT where B is defined as the equivalent width of the power spectrum given by

1 BTτ = (6.4) c 2

Then B in Eq. (6.4) can be expressed by

1 B = (6.5) 2τ cT

Substituting Eq. (6.5) into Eq. (6.3),

∆ ≥ ατ c (6.6)

where the product ατ c is referred to as the “zero correlation time” and τ c is the coherence time. Therefore, α is defined as the factor. T is the sampling period.

Zeiler et al. (1978) analyzed the steady state behavior of the ALE for a stationary input consisting of multiple sinusoids in white noise and were the first to study the effect of various choices of the delay ( ∆ ) on the steady state response of the ALE. They also derived a relation for the value of ∆ to yield a deep notch in the transfer function of the

ALE for the case of two sinusoids. The relation is given by

L −1 ∆ +=+∆(1/2)/nf (6.7) 2 where L is the length of the ALE, ∆f is the difference between the two frequencies of the input sinusoids, and n is any nonnegative integer and satisfies

(nfL+ 1/2)/∆> ( − 1)/2 (6.8)

Reddy et al. (1981) showed that there exists an optimum value of the delay parameter ∆ for a single sinusoid. They proposed an iterative method to find the optimal

∆ for a given data set. The iterative method involves computing the spectrum of the data and is computationally expensive. The optimal decorrelation parameter will give sharpness at the frequency of sinusoid in the power spectral density, which indicates good

62 estimation of sinusoid. In order to find the optimum value of ∆ for the ALE with the

Tapped Delay Line (TDL) structure, they differentiated the average error variance with respect to ∆ . The stationary points are thus given by

ω0 (Lkk+ 2∆− 1) = π integer (6.9)

where ω0 (rad/s) is the frequency of the input sinusoid.

Egardt et al. (1983) extended the idea proposed by Reddy et al. (1981) to find the optimal ∆ for the case of two sinusoids. An assumption that the noise variance is small compared to the signal variance is made when the residual variance is differentiated with respect to ∆ . The result is given by

2(1)nLπ − ∆= − , n integer (6.10) ω 2

where ω =−ωω12, ω1 and ω2 are the angular frequencies of the two sinusoids.

Reddy et al. (1981) and Egardt et al. (1983) found that the ALE with their near optimum values of ∆ gives not only sharper spectral estimates but also an unbiased estimate of the sinusoid frequency. They set the initial value of ∆ as unity, and then carried out a series of recursions to find the optimum value of ∆ . The function, G()ω 2 , was used as the performance measure of the ALE as a spectral estimator and many simulations were provided to demonstrate that the ALE with near-optimum ∆ yields substantial improvements in the estimates of the unknown sinusoidal frequencies. Reddy et al. also derived the optimum value of ∆ for the ALE with lattice form.

Reddy et al. (1981) and Egardt et al. (1983) derived the optimal choices of ∆ for one and two sinusoids under the assumption of high SNR. Gupa (1985) derived the optimal value of ∆ for arbitrary SNR in the case of a single sinusoid. Yoganandam et al.

(1988) derived the optimal value of ∆ for arbitrary SNR in the case of two sinusoids.

They proposed a method based on the mean square error of the ALE, which is the

minimum when ∆ = ∆ opt . The relation is given by

nπ ∆=(1)/2 −+L opt δω nL even for δω< π (6.11) nLodd for π <<δω 2 π

where δωω=−21 ω, ω1 and ω2 are the angular frequencies of the two sinusoids. They derived expressions for predicting the bias in the frequency estimates for one and two sinusoids, both with the usual choice of ∆ (i.e., ∆ = 1), and with the near-optimum choice. The numerical results show that the frequency estimates obtained with near- optimum choice of ∆ are superior with respect to bias, variance, and threshold SNR than the estimates produced with ∆ = 1.

The optimal value of the delay parameter for three sinusoids corrupted by white noise has not been investigated. The formula used to compute the optimal value is not derived in this dissertation because of the computational complexity. However, simulations are performed to determine the optimal delay parameter for three sinusoids corrupted by white noise. These simulations can be a guide to select optimal delay parameter for three sinusoids corrupted by white noise and provide an introduction for further work. These simulations and analyses are discussed in Appendix A.

Delay Parameter for Manatee Problem

For the manatee problem, the manatee vocalizations are not a completely combinations of several sinusoids and the background noise are not white noise. From the figures shown in Chapter 2 (Figure 2-2, Figure 2-3, Figure 2-5, and Figure 2-6), the

64 manatee vocalizations are narrow band signals compared to background noise.

Therefore, it is possible to use ALE to reduce the background noise of manatee vocalizations. However, it is important to choose the proper delay parameter, order, and step size of adaptive filter before implementing the ALE to reduce the background noise.

If p( j) represents the cross correlation between a signal and the delayed version of itself, and r( j ) represents the autocorrelation of that signal, then

p()jExkxkj= [′ ()(+ )] (6.12)

rj()= Exkxk [()(+ j )] (6.13) where x(k) represents the observed manatee vocalizations corrupted by background noise and x′(k ) is the delayed version of x(k ) . Therefore,

xk′()= xk (−∆ ) (6.14)

Substituting the Eq. (6.14) into Eq. (6.12), we can get

p()j= Exk [(−∆ )( xk + j )] (6.15)

Therefore, the relationship of p( j ) and r( j ) is given by

p()jr= (∆+ j ) (6.16)

For the ALE algorithm, p( j ) will be the cross correlation between the primary input, x(k) , and the reference input, a delayed version of x(k ) .

The real data of a typical manatee call, natural noise, and boat noise are used to calculate their autocorrelations. These three autocorrelations are shown in Figure 6-1(a),

Figure 6-1(b), and Figure 6-1(c), respectively. The results show that the envelope of the autocorrelation of the manatee call still remains high as j increases because of its periodic natural, but the autocorrelation of the noise, including natural noise and boat noise,

65 decreases rapidly as j increases. Although the autocorrelation of noise is small enough when j = 20 , simulation results show that the delay is not optimal to reject the boat noise from the narrow band output of ALE. Likewise, although the delay parameter, ∆ , is large enough to decorrelate white noise with ∆ = 1, the simulations show that the ALE with optimal or near-optimal value (much larger than 1) of ∆ yields a much better estimate of the sinusoid frequency (Reddy et al., 1981; Egardt et al., 1983). Different manatee calls need a different delay to obtain the best performance; therefore it is difficult to find a delay that is the best one for every call. However, it is possible to find a range of delay that can provide good performance. From Figure 6-1, it can be found that the delay parameter between 100 and 300 should be large enough to decorrelate the background noise of manatee vocalizations. The discussions in the section of simulation results in terms of SNR show that proper delay should be a value between 100 and 300 which provide a best SNR of the superposed signal after FIR-ALE or FALE is applied.

x 10-3 8

(a) 6

Autocorrelation r() j -2

-4

-6 -300 -200 -100 0 100 200 300 Time step j

x 10-5 7

6 (b)

1 Autocorrelation r( j ) j r( Autocorrelation 0

-1

-2 -300 -200 -100 0 100 200 300 Time step j

x 10-4 2.5

1.5

0.5

0 Autocorrelation r( j ) j r( Autocorrelation

-0.5

-1 -300 -200 -100 0 100 200 300 Time step j Figure 6-1. Autocorrelation of manatee vocalizations and background noise. (a) pure manatee vocalization, (b) natural noise and (c) boat noise.

Review of Optimal Order and Step Size

The order of adaptive filter is another important factor that affects the performance of ALE. Rickard and Zeidler proposed that increasing the filter length will narrow the filter pass band about the center frequency, thus improving the estimate of signal amplitude for a given SNR of the input (Rickard and Zeidler, 1979). However, the misadjustment, defined as the dimensionless ratio of the average excess MSE to the minimum MSE, scales with the order of the adaptive filter. The theoretical expression for misadjustment is given by Eq. (4.25). The SNR of output is limited due to the

67 unavoidable misadjustment noise of the ALE. If the order of the adaptive filter is too low, it cannot provide an accurate estimate for the underlying process. Therefore, the optimal order should be the one that not only provides accurate estimates but also limits large misadjustment.

Nehorai and Malah (1980) derived the optimal order of the ALE for a given step size aiming at maximizing the SNR gain, not minimizing the MSE. When the adaptation time-constant was specified and with the practical assumption that the N sinusoidal

components have equal power and µPx L << 1, the relationship between step size µ and order L was given by

1/2 LNPopt≅ [2 /(µ x )] (6.17)

where N is the number of sinusoids and Px is the total power of the input signal. For N

equal power sinusoids in white noise, the adaptation time-constant τ w is given by

22 τ wn=+1/[2µσ ( (LN /2 ) σ s )] (6.18)

2 2 where σ s is the total power of the N sinusoidal signals and σ n is the noise power. In practice, L is set to the maximum of L , and µ is then determined to satisfy the relationship in Eq. (6.18) (Nehorai and Malah, 1980). All of results also can be used as guidelines for choosing the ALE parameters when the N sinusoidal components of the input signal do not have equal power.

Order for Manatee Problem

Although the results derived by Nehorai and Malah (1980) can be used as guidelines for choosing the order of ALE to reduce the background noise of manatee vocalizations, it still cannot be used to accurately estimate the optimal order for the

68 manatee problem. The frequency spectrum of one of the manatee calls (category 1110) in the library is shown in Figure 6-2. The instantaneous transfer function of the adaptive filter between the reference input and narrow band output during the manatee call period is shown in Figure 6-3 when the order of FIR-ALE is set to 70. Figure 6-3 suggests that the transfer function of FIR-ALE can approximately match the frequency response of that manatee vocalization.

110

100

Magnitude (dB) 40

10 0 5 10 15 20 Frequency (kHz) Figure 6-2. Power spectrum of a typical manatee vocalization (from category 1110).

-10

-20

-30

Magnitude (dB) -40

-50

-60 0 5 10 15 20 25 Frequency (kHz) Figure 6-3. The instantaneous transfer function of FIR-ALE during the manatee call period when the order of adaptive filter is set to 70.

When the order of the FIR-ALE is reduced to 20, the instantaneous transfer function of the adaptive filter between the reference input and narrow band output during

69 the manatee call period is shown in Figure 6-4. It is obvious that the transfer function cannot match the frequency response of that manatee vocalization. However, the adaptive filter provides approximately a 0 dB gain at the largest peak frequency of the manatee call. This means that the adaptive filter passes the most energy of the manatee vocalization during the period of that manatee vocalization.

-5

-10

-15

-20

-25 Magnitude (dB) Magnitude

-30

-35

-40 0 5 10 15 20 25 Frequency (kHz) Figure 6-4. The instantaneous transfer function of FIR-ALE during the manatee call period when the order of adaptive filter is set to 20.

The instantaneous transfer function of FIR-ALE outside the period of the manatee call is shown in Figure 6-5 when the order of adaptive filter is set to 20. The adaptive filter provides a -25 dB gain outside the period of the manatee call. The misadjustment of the ALE, including FIR-ALE and FALE, with order of 20 is smaller than that of ALE with order of 70. Furthermore, higher order increases the computational complexity of

ALE. The maximum number of the dominant harmonics of manatee vocalizations is not larger than 4. Therefore, the order of 20 is probably large enough to estimate most manatee vocalization. Therefore, the orders of FIR-ALE and FALE are both set to 20 in following simulations in order to compare them equally.

-10

-15

-20

-25

-30

-35

Magnitude (dB) -40

-45

-50

-55 0 5 10 15 20 25 Frequency (kHz) Figure 6-5. The instantaneous transfer function of FIR-ALE outside the period of the manatee call when the order of adaptive filter is set to 20.

Variable Step Size ALE

The step size of the adaptive filter is a critical factor that affects the tracking ability, convergence rate, misadjustment, and stability margin of the adaptive filter. Some algorithms that are aimed at speeding up convergence accomplish this at the expense of increased computational complexity, such as lattice structure, RLS algorithm, and so on.

The strategy of variable step size of ALE is investigated to reduce the background noise of manatee vocalizations in this dissertation. The normalized LMS algorithm is proposed to solve the gradient noise amplification problem the LMS filter suffers from, when the input is large. The weights update for LMS algorithm with normalized step size is given by

µ Ak(+= 1) Ak () + X()() kek (6.19) δ + Xk()2 where µ represents the adaptation constant and δ represents a positive constant to prevent the step size from becoming too large when the tap-input power is small.

However, if a variable step size is implemented for manatee problem, the step size should be large during manatee vocalizations for good tracking and small during the rest

71 periods for a small misadjustment. However, the strategy of normalized LMS operates in an opposite manner and is not suitable to improve the performance of ALE. Although the strategy of normalized LMS aims at preventing the system diverge, the performance of normalized LMS is worse than fixed step size LMS, especially when the SNR of manatee vocalizations is high. Therefore, it is not suitable to use normalized LMS to reduce the background noise. A mechanism should be used to control the magnitude of the signal measured by hydrophone so that it can maintain the system enhanced by fixed step size

LMS stable.

Other strategies to control step size are also studied to meet the special requirement for the manatee problem. The strategy of computing the autocorrelation of the reference input is used to adjust the step size. However, this strategy cannot provide the proper step size for each period when the SNR of the manatee vocalizations is low.

Furthermore, the step size controlled by this strategy is very sensitive and makes it easier for the system to diverge. When the SNR of manatee vocalizations is high, the benefits of this strategy are very small. The simulation results show that the performance of ALE, including FIR-ALE and FALE, based on the variable step size obtained by autocorrelation of the reference input is not better than ALE with fixed step size.

Furthermore, these strategies increase the computational complexity. Therefore, the step size for FIR-ALE and FALE are set to 0.1 and 1, respectively.

Feedback Constant

From Figure 4-5 in Chapter 4, if β = 0 , the FALE reduces to the FIR-ALE. There exists a range of β that presumably makes the FALE superior to the FIR-ALE. The simulations implemented by Glover and Chang (1989) show that the “optimum” value of

β varies from 0.4 for high SNR cases to somewhat less than 0.9 for lower SNR cases.

For β < 0.4 , the impact of the feedback within the systems is not readily apparent, while for β > 0.9 , the estimation error is increased by the adaptation oscillations due to feedback. They suggested that the FALE provide lowest average sum of the squared error for different SNR when the feedback is 0.85. Therefore, the feedback constant β is set to 0.85 in this dissertation.

The values of the parameters selected for the following simulations are shown in the Table 6-1. The bandpass filter used as the preprocessing for FIR-ALE and FALE are the same as the bandpass filter used as the baseline for comparison.

Table 6-1. Parameters of ALE (FIR-ALE and FALE) for the simulations. Step size Feedback Preprocessing Delay ( ∆ ) Order ( µ ) constant FIR-ALE Bandpass filter 300 0.1 20 0 FALE Bandpass filter 300 1 20 0.85

Simulation Results in Time Domain

The simulation results based on the library of manatee vocalizations in the time domain are shown in this section. As stated in Chapter 5, the library of manatee vocalizations has 100 manatee calls. In order to test the performance of FIR-ALE and

FALE, these calls are organized into 20 WAV files. Each file has five manatee calls with the same intervals between these calls. The selection of time is dependent on the convergence rate of the FIR-ALE and FALE and the memory of the computer for simulation. The sampling frequency of the observed manatee vocalizations is 48 kHz.

Simulations show that 1.3 second is enough for FIR-ALE and FALE to converge. If this interval is set too large, it will take a long time for the computer to process the data and more memory to store the variables. Therefore, the intervals between these manatee

73 vocalizations are set to 1.3 second. The time before the first manatee vocalization and the time after the last one are also set to 1.3 second (see Figure 6-6(a)).

0.5 (a) 0.5 (b)

0 0

-0.5 -0.5

-1 Natural noises -1 Pure manateecall 0 2 4 6 8 0 2 4 6 8 Time (seconds) Time (seconds)

0.5 (c) 0.5 (d)

0 0

-0.5 -0.5 Boat noise -1 -1 0 2 4 6 8 0 2 4 6 8 Time (seconds) Snapping shrimpnoise Time (seconds)

0.5 (e)

-0.5

superposed signal -1 0 2 4 6 8 Time (seconds)

Figure 6-6. Manatee vocalizations and background noise in time domain. (a) pure manatee vocalizations, (b) natural noise, (c) boat dominated noise, (d) snapping shrimp noise and (e) superposition of manatee calls, natural noise, boat dominated noise, and snapping shrimp noise.

Typical manatee calls (category 1000), natural noise, boat noise, snapping shrimp noise, and the numerical superposition of these four signals in time domain are shown in

Figure 6-6(a-e), respectively. The advantage of numerical superposition is that it is easy to obtain manatee vocalizations with arbitrary and known SNR in simulations. The performance of FIR-ALE and FALE for acoustic superposition data will be shown later.

The superposed signals after the band pass filter, FIR-ALE, or FALE is applied are shown in Figure 6-7(a), Figure 6-7(b), and Figure 6-7(c), respectively. As state earlier, the original manatee vocalizations are preprocessed by the bandpass filter before the FIR-

ALE or FALE is applied. Therefore, to be more accurate, the superposed signal shown in

Figure 6-7(b) should be the signal after bandpass filter and FIR-ALE are applied and the superposed signal shown Figure 6-7 (c) should be the signal after bandpass filter and

FALE are applied. However, in order to make the description clear and simple, the signal shown in Figure 6-7(b) and Figure 6-7(c) are called the superposed signal after FIR-ALE and FALE is applied, respectively. A purely qualitative visual comparison of these results indicates that FALE is most effective at improving the SNR.

(a) 0.5

-0.5

-1 0 2 4 6 8 After bandpass filter is applied Time (seconds)

0.2 (b)

0.1

-0.1

-0.2

After FIR-ALE is applied 0 2 4 6 8 Time (seconds)

0.2 (c)

0.1

-0.1

-0.2 After FALE is applied 0 2 4 6 8 Time (seconds) Figure 6-7. Performance of bandpass filter, FIR-ALE, and FALE in time domain. (a) after the band pass filter is applied, (b) after FIR-ALE is applied and (c) after FALE is applied.

The spectrogram of the original five manatee calls corrupted by background noise is shown in Figure 6-8. The spectrogram of the five manatee calls after band pass filter,

FIR-ALE, and FALE is applied are shown in Figure 6-9, Figure 6-10, and Figure 6-11, respectively. From these figures, the background noise is significantly reduced by both

ALE algorithms. However, the superior performance of FALE over FIR-ALE is not so obvious. In this simulation, only five manatee vocalizations are used to test the performance of these two ALE algorithms. In order to test them more completely, all the vocalizations in the library are used to evaluate the performance of FIR-ALE and FALE.

However, the simulation results are only shown in terms of SNR. No power spectrums and spectrograms of manatee vocalizations before or after ALE is applied will be shown in the next section.

120

20 100

15 80

60 10 Frequency (kHz) Frequency 40

5 20

0 0 1 2 3 4 5 6 7 8 9 Time (seconds) Figure 6-8. Spectrogram of the five original manatee calls.

120

20 100

15 80

10 40 Frequency (kHz) Frequency

5 20

0 0 0 1 2 3 4 5 6 7 8 9 Time (seconds) Figure 6-9. Spectrogram of the manatee calls after band pass filter is applied.

120

20 100

15 80

10 40 Frequency (kHz) Frequency

5 20

0 0 0 1 2 3 4 5 6 7 8 9 Time (seconds) Figure 6-10. Spectrogram of the manatee calls after FIR-ALE is applied.

120

20 100

15 80

60 10 40 Frequency (kHz) Frequency

5 20

0 0 0 1 2 3 4 5 6 7 8 9 Time (seconds) Figure 6-11. Spectrogram of the manatee calls after FALE is applied.

Simulation Results in Terms of SNR

In this section, the performances of both FIR-ALE and FALE are compared in terms of SNR. In general, the SNR should be computed from the noise and signal during the same interval. However, after filtering, the residue background noise cannot be separated from the manatee call; hence it is not possible to distinguish the residue noise and the manatee call during the time interval of the manatee call. Furthermore, in the detection part of the system, the processed manatee vocalizations and the residue noise outside of the time interval vocalizations are compared to the threshold, not the residue noise during the period of the manatee vocalizations. Therefore, a modified definition of

SNR is used in this dissertation.

In practice, there exist two cases for the signal observed by a hydrophone. One is when only background noise is present, which is shown in Figure 6-12(b). The other is that the hydrophone measures not only background noise but also a manatee call, which results in the superposition of the signals shown in Figure 6-12(a) and Figure 6-12(b).

Five pure manatee calls and superposed background noise are shown in Figure 6-12(a)

and Figure 6-12(b), respectively. SNRori is defined as the estimated SNR of the original

manatee call corrupted by background noise. As shown in Figure 6-12, SNRori is computed by taking the Root Mean Square (RMS) value of the time domain signal in the region where the pure manatee call is present and dividing that value by the RMS value over the same time interval just prior to the call where only the background noise is present. It is assumed that the background noise levels do not vary significantly over the duration of a manatee call. Hence, the same method is used to estimate the SNR of the manatee call after filtering (see Figure 6-13). As a result, the residue noise during the

78 interval of the manatee call is unavoidably added to the true signal power. Therefore, the

SNR of the manatee call after filtering is biased.

1 (a) 0.5

-0.5 RMS v alue of the manatee call in this period Pure manatee call -1 0 1 2 3 4 5 6 7 8 9 Time (seconds)

1 (b) RMS v alue of the noise 0.5 in this period

-0.5

-1 0 1 2 3 4 5 6 7 8 9 Superposed background noise Time (seconds) Figure 6-12. The method used to compute the SNR of an original manatee call. (a) pure manatee call and (b) background noise.

0.2 (a) 0.1

-0.1 RMS v alue of the manatee call in this period

After FALE is applied -0.2 0 1 2 3 4 5 6 7 8 9 Time (seconds)

0.2

RMS v alue of the noise (b) 0.1 in this period

-0.1

-0.2

Residue background noise 0 1 2 3 4 5 6 7 8 9 Time (seconds) Figure 6-13. The method used to compute the SNR of the manatee call after filtering. (a) superposed signal of pure manatee call and background noise after FALE is applied and (b) background noise after FALE is applied.

In order to evaluate the performance of the bandpass filter, FIR-ALE, and FALE versus SNR of original manatee vocalizations ranging from -25 dB to 0 dB, numerical superposition is used to obtain the noise corrupted manatee vocalizations. The

79 performance of the bandpass filter, FIR-ALE, and FALE for acoustic superposition of manatee vocalizations and background noise will be verified later using the real recordings made by O’Shea (1981-1984).

The library of 100 manatee calls is used in the simulations to rigorously test these three algorithms. In simulations, the database of the manatee call is organized into 20 recordings. Each recording has five manatee calls. Therefore, each category has two recordings. In order to equally test each category, the background noise used is the same for each recording. However, the background noise is different for five manatee calls

within one recording. In order to equally compare performance, SNRori is set to -5 dB for all manatee calls. The SNR of manatee calls after application of the band pass filter,

FIR-ALE , and FALE is applied is shown in Figure 6-14, Figure 6-15, and Figure 6-16, respectively. From these three figures, it can be seen that the variance of the performance of FALE for each manatee call is the largest among all three algorithms. The possible reasons for that variance include: (1) difference in frequency characteristic of each call, even for the calls within the same category; (2) background noise is nonstationary.

45 0000 1000 1010 1011 1100 1110 1111 1200 1210 1211 40

10 After bandpass filter is applied (dB) 5

0 0 10 20 30 40 50 60 70 80 90 100 Number of the manatee vocalizations Figure 6-14. SNR of each manatee vocalization after band pass filter is applied when is equal to -5 dB. SNR ori

45 0000 1000 1010 1011 1100 1110 1111 1200 1210 1211 40

After FIR-ALE is applied (dB) 10

0 0 10 20 30 40 50 60 70 80 90 100 Number of the manatee vocalizations Figure 6-15. SNR of each manatee vocalization after FIR-ALE is applied when is SNR ori equal to -5 dB.

45 0000 1000 1010 1011 1100 1110 1111 1200 1210 1211 40

15 After FALE is applied (dB) 10

0 0 10 20 30 40 50 60 70 80 90 100 Number of the manatee vocalizations Figure 6-16. SNR of each manatee vocalization after FALE is applied when is SNR ori equal to -5 dB.

The difference in the SNR of the FALE versus the FIR-ALE for each manatee call is shown in Figure 6-17. There are only five manatee calls (out of 100) for which the performance of the FALE is worse than that of the FIR-ALE when the SNR of original manatee vocalizations is -5 dB, which means the performance of the FALE is worse than that of the FIR-ALE for 5% calls. A qualitative inspection suggests that this is caused by the relatively large changes in the characteristic frequencies for four of the manatee calls and no clearly discernable harmonic frequencies for the other manatee call.

14 0000 1000 1010 1011 1100 1110 1111 1200 1210 1211 12

-2

-4 Improvement of the FALE over FIR-ALE (dB)

-6 0 10 20 30 40 50 60 70 80 90 100 Number of the manatee vocalizations Figure 6-17. SNR improvement of the FALE compared to FIR-ALE for each manatee vocalization when is equal to -5 dB. SNR ori

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Percentage for which FALE is worse than FIR-ALE 0 -25 -20 -15 -10 -5 0 SNR (dB) ori Figure 6-18. Percentage for which the performance of FALE is worse than that of FIR- ALE.

However, the percentage increases as the SNR of manatee calls decreases, which is shown in Figure 6-18. The chosen settings of the FALE cannot adequately track the variation of the manatee call, especially when the SNR of the manatee call, after band pass filtering, is very low. As discussed earlier, the tracking ability of the FALE is worse than that of the FIR-ALE because of the feedback constant. From Eq. (4.26) in Chapter 4, the weight in front of the primary input is small when the feedback constant β is set to a large value. Thus, it is no surprise that each manatee call has a different optimal step size

82 and feedback constant. Due to practical considerations, it is very important to select a fixed β with a corresponding proper step size for FALE, which not only facilitates tracking a nonstationary signal but also maintains stability.

Using the notation that the average SNR of each original manatee call category is

represented by SNR ori , the performance of the band pass filter, FIR-ALE, and FALE for the manatee calls in each category and the overall average are shown in Table 6-2. The average SNR of the original manatee call for each category is given by,

10 10 22 SNRori=× 10 log 10 [(∑∑PQij ) /( )] (6.20) ij==11

th where Pi represents the RMS value of the i manatee call for a particular category and

th Qj represents the RMS value of the j noise component. Likewise, the method to compute the average SNR of the processed manatee calls after these three enhancement

algorithms are applied is the same as that used to compute SNR ori . GFIR- BPF and

GFALE- BPF , represent the gain or SNR improvement of FIR-ALE and FALE over the band

pass filter, respectively. GFALE- FIR represents the SNR improvement of the FALE over

FIR-ALE. These simulation results show that both the FIR-ALE and FALE are effective at reducing the background noise of a manatee call. The average performance of the

FALE is about 21.9 and 5.4 dB better than that of the bandpass filter and FIR-ALE, respectively. From Table 6-2, it is seen that the performance of these two algorithms for category 0000, (manatee calls with no clearly discernable harmonics) is a little worse than the others. The improvement of FALE over FIR-ALE for this category is also smaller than others categories of calls.

Table 6-2. The average performance of bandpass filter, FIR-ALE and FALE for the manatee calls corresponding to each category (dB). Category After After After G G G SNR ori bandpass FIR-ALE FALE FIR-BPF FALE-BPF FALE-FIR 0000 -5.0 4.0 14.9 17.8 10.9 13.8 2.9 1000 -5.0 4.1 22.0 27.6 17.9 23.5 5.6 1010 -5.0 3.8 18.5 24.3 14.7 20.5 5.8 1011 -5.0 4.3 21.5 27.2 17.2 22.9 5.7 1100 -5.0 4.4 21.9 27.7 17.5 23.3 5.8 1110 -5.0 4.4 20.7 26.3 16.3 21.9 5.6 1111 -5.0 4.1 21.0 26.2 16.9 22.1 5.2 1200 -5.0 3.9 21.0 26.8 17.1 22.9 5.8 1210 -5.0 3.8 17.5 23.0 13.7 19.2 5.5 1211 -5.0 4.2 21.6 26.5 17.4 22.3 4.9 Average -5.0 4.1 20.6 26.0 16.5 21.9 5.4

To further assess the performance of each filter for different levels of background

noise, the band pass filter, FIR-ALE, and FALE are compared when SNR ori varies from

-25 dB to 0 dB. The performance of each filter are shown in Figure 6-19(a), Figure 6-

19(b), and Figure 6-19(c), respectively. The results indicate that as the SNR of the original manatee call is reduced, the noise reduction performance of all algorithms is also reduced. The best performance is again achieved by the FIR-ALE and the FALE for manatee calls with one dominant frequency (category 1000), while the worst performance is achieved for manatee calls without distinct harmonic frequencies. As shown in Figure

6-19(a), the SNR improvement of the band pass filter does not vary significantly from one category to the next as the background noise level is changed. However the FIR-

ALE and FALE is dependent on the category of the manatee call selected as the background noise level is changed (see Figure 6-19(b) and Figure 6-19(c)).

10 0000 9 1000 (a) 8 1010 1011 7 1100 1110 6 1111 5 1200 1210 4 1211

-1

SNR ofmanatee calls after bandpass filteris applied(dB) -25 -20 -15______-10 -5 0 SNR (dB) ori 35 0000 (b) 1000 30 1010 1011 25 1100 1110 20 1111 1200 1210 15 1211

0 SNR ofmanatee calls after FIR-ALE is applied (dB) -25 -20 -15______-10 -5 0 SNR (dB) ori 40 0000 (c) 35 1000 1010 30 1011 1100 25 1110 1111 1200 20 1210 1211 15

0 SNR of manatee calls after FALE is applied (dB)

-25 -20 -15______-10 -5 0 SNR (dB) ori Figure 6-19. Performance of bandpass filter, FIR-ALE, and FALE. (a) SNR of manatee calls after band pass filter is applied for each category and various SNR, (b) SNR of manatee calls after FIR-ALE is applied for each category and various SNR and (c) SNR of manatee calls after FALE is applied for each category and various SNR.

Additional simulations are performed with the average SNR over ten categories to further evaluate the relative performance of the FIR-ALE and FALE algorithms. The overall average SNR of the original manatee calls, for all ten categories is given by,

100 100 22 Average of SNRori=× 10 log 10 [(∑∑PQij ) /( )] (6.21) ij==11

Likewise, the method to compute the average SNR of the processed manatee calls after these three enhancement algorithms are applied, is the same as that shown in Eq. (6.21).

From Figure 6-19, the SNR of manatee vocalizations after filtering is still around 0 dB for the original manatee vocalizations with low SNR just because the residue noise during the period of manatee vocalizations is taken as part of the manatee vocalizations.

As stated earlier, the residue noise during the manatee vocalizations period cause a bias for computing the SNR of manatee vocalizations after filtering. Although the residue noise during the manatee vocalizations can be thought of as a part of manatee vocalizations, when the processed manatee vocalizations after ALE is applied is further processed by detection part, the energy of the residue noise will be distributed to a broad frequency range, not like the energy of manatee vocalizations only distributed to several frequencies. Therefore, the energy of the residue noise cannot be completely thought as an addition to the SNR of the manatee vocalizations from the detection aspect because the detection method compares the FFT results of processed manatee vocalizations. The

SNR of manatee vocalizations after filtering gives an upper bound for the performance of

FIR-ALE and FALE due to the bias. The upper bound of overall performance comparison between the band pass filter, FIR-ALE, and FALE as a function of the SNR

and the performance comparison between them, when the average of SNRori over ten

86 categories varies from -25 dB to 0 dB, are shown in Figure 6-20 and Figure 6-21, respectively.

35 After bandpass filter After FIR-ALE 30 After FALE

10 SNR after filtering (dB)

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori Figure 6-20. Upper bound of overall performance comparison between the band pass filter, FIR-ALE, and FALE as a function of the SNR.

30 Improvement of FIR-ALE over bandpass filter Improvement of FALE over bandpass filter 25 Improvement of FALE over FIR-ALE

15 Gain (dB) Gain 10

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori Figure 6-21. Performance gains of the various algorithms using the same band pass filter as a baseline as a function of the SNR for the upper bound case.

From Figure 6-21, it is seen that the SNR improvement achieved by the FIR-ALE

and FALE compared to the band pass filter increases as the average of SNRori is increased. The improvement of the FALE over FIR-ALE becomes progressively larger

when the average of SNR ori is increased for low values of SNR up to -9 dB. This result is in agreement with the results by Chang (1993).

The simulation results indicate that the performance of FALE is 5.4 dB better than that of FIR-ALE when the step size is carefully selected and the perturbations are not too large. However, in practice, the step size must be selected to provide a sufficient stability margin in order to avoid the instability due to large perturbations.

If the residue noise during the manatee call period is deducted (see Figure 6-13), this gives a lower bound for the improvement of ALE. The lower bound of the overall performance comparison between the band pass filter, FIR-ALE, and FALE as a function

of the SNR and the performance comparison between them, when the average of SNRori over ten categories varies from -25 dB to 0 dB, are shown in Figure 6-22 and Figure 6-

23, respectively. The superposed signal after the bandpass filter is applied is about 6 dB better than the original signal. There is no improvement of FIR-ALE and FALE over bandpass filter when the SNR of the original manatee vocalizations is -25 dB.

40 After bandpass filter After FIR-ALE 30 After FALE

0 SNR (dB) filtering after -10

-20

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori Figure 6-22. Lower bound for overall performance comparison between the bandpass filter, FIR-ALE, and FALE as a function of the SNR of the original manatee call.

The lower bound and upper bound for the performance of bandpass filter, FIR-

ALE, and FALE is shown in Figure 6-24. From this figure, the difference between the lower bound and upper bound becomes large as the SNR of the original manatee vocalizations decreases.

30 Improvement of FIR-ALE over bandpass filter Improvement of FALE over bandpass filter Improvement of FALE over FIR-ALE 25

15 Gain (dB) Gain 10

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori Figure 6-23. Performance gains of the various algorithms using the same bandpass filter as a baseline as a function of the SNR for lower bound case.

After bandpass filter (Lower bound) 40 After bandpass filter (Upper bound) After FIR-ALE (Lower bound) After FIR-ALE (Upper bound) 30 After FALE (Lower bound) After FALE (Upper bound) 20

0 SNR after filtering (dB)SNR filtering after

-10

-20

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori

Figure 6-24. Lower bound and upper bound for the performance of bandpass filter, FIR- ALE, and FALE.

For the manatee problem, the delay must be large enough to decorrelate the background noise and still keep the manatee call highly correlated. The final goal for the manatee problem is to improve the SNR of the narrowband output of the adaptive filter

89 and then reduce the rate of the missing calls and false calls. The SNR after ALE is applied is used to evaluate the performance of each delay. The lower bound and upper bound of the performance of the bandpass filter, FIR-ALE and FALE with the delay from

10 to 3000 when the SNR of original manatee vocalizations is -5 dB is shown in Figure

6-25 and Figure 6-26, respectively. From these two figures, the delay with a value between 100 and 300 can provide a best SNR of the superposed signal after FIR-ALE or

FALE is applied.

35 After bandpass filter After FIR-ALE 30 After FALE

10 SNR after filtering (dB) SNRfiltering after

1 2 3 10 10 10 Delay Figure 6-25. Lower bound of the performance of the bandpass filter, FIR-ALE and FALE with the delay from 10 to 3000 when the SNR of original manatee vocalizations is -5 dB.

35 After bandpass filter After FIR-ALE 30 After FALE

10 SNR after filtering (dB)

1 2 3 10 10 10 Delay Figure 6-26. Upper bound of the performance of the bandpass filter, FIR-ALE and FALE with the delay from 10 to 3000 when the SNR of original manatee vocalizations is -5 dB.

Results on Acoustic Superposition of Manatee Vocalizations

In previous discussion, only a numerical superposition of the manatee vocalizations and background noise is used to evaluate the performance of bandpass filter, FIR-ALE, and FALE in time domain and in terms of SNR. The performances of these three algorithms for acoustic superposition of manatee vocalizations and high-level background noise are shown in Figure 6-27. Three manatee vocalizations are audible in this recording.

0.5 (a)

-0.5 Original signal 0 1 2 3 4 5 6 7 8 9 Time (seconds)

0.5 (b)

-0.5 0 1 2 3 4 5 6 7 8 9 After bandpass filter Time (seconds)

0.5 (c)

-0.5 After FIR-ALE 0 1 2 3 4 5 6 7 8 9 Time (seconds)

0.5 (d)

0 After FALE -0.5 0 1 2 3 4 5 6 7 8 9 Time (seconds)

Figure 6-27. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and high-level background noise. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

The performances of these three algorithms for another acoustic superposition of manatee vocalizations and low-level background noise are shown in Figure 6-28. Two

91 manatee vocalizations are audible in this recording. The performance of the FIR-ALE and FALE on acoustic superposition of manatee vocalizations is pretty good, especially when the SNR of the original manatee vocalizations is high (see Figure 6-28).

0.5 (a)

-0.5 Original signal 0 2 4 6 8 10 Time (seconds)

0.5 (b)

-0.5 0 2 4 6 8 10 After bandpass filter Time (seconds)

0.5 (c)

-0.5 After FIR-ALE After 0 2 4 6 8 10 Time (seconds)

0.5 (d)

0 After FALE After -0.5 0 2 4 6 8 10 Time (seconds)

Figure 6-28. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and low-level background noise. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

These two noise corrupted manatee vocalizations are selected from the recordings made by O’Shea (1981-1984). However, the SNR of the manatee vocalizations in the recordings made by O’Shea are unknown and fixed. Therefore, no more discussions about the performance of FIR-ALE and FALE for these recordings (acoustic superposition of manatee vocalizations and background noise) will be presented in this dissertation.

Field Test

In order to show the performance of bandpass filter, FIR-ALE, and FALE for a set manatee vocalizations with different SNR, a field test is performed to obtain the acoustic superposition of manatee vocalizations and background noise.

Description of Field Test

A land based experiment was conducted to obtain acoustic recordings that are not a numerical superposition of previously recorded manatee vocalizations and background noise. For this experiment, two audio speakers are used. One speaker is used to broadcast a recording of ten manatee vocalizations (one from each category) that are separated by two second intervals. This speaker is denoted as the “manatee speaker”.

The second speaker is used to broadcast sound from a recording of a boat operating at high speed. The boat noise has essentially uniform sound power emission and is continuous. The second speaker is denoted as the “boat noise speaker”.

The recordings were played by using two MP3 players. The output of each MP3 layer was amplified by using two audio amplifiers. For the boat noise, the volume of the

MP3 player and the gain of the amplifier were set to maximum. The resulting boat noise audio signal had an overall SPL approximately equal to 88 dB (referenced to 20 micro-

Pascals) when measured 5 ft from the source. Qualitatively speaking, the output of the speaker producing the boat noise was very loud. The broadcast level for the manatee vocalizations were adjusted such that when the two speakers were placed at the same position with respect to the microphone, the vocalizations were barely discernable to the human ear.

Twenty seven different tests were conducted. A single microphone measuring the acoustic signal was positioned 6 ft. from the ground and the speakers were located

93 approximately 2 ft. from the ground. Both speakers were oriented to directly face the microphone. For each test, the volume setting of each MP3 player and the gain of each amplifier was unchanged. However, for each of the 27 different tests, the manatee speaker and the boat noise speaker were placed in different positions. All possible combinations of speaker distances were measured for the following horizontal positions:

(5 ft., 25 ft., 50 ft., 75ft., and 100 ft.). For example, for one test the manatee speaker was placed at a distance 5ft. from the microphone and the boat noise speaker was also placed at a distance 5 ft. (speakers side by side) from the microphone. Boat noise was broadcast, the data acquisition equipment was triggered, and then the manatee recordings were broadcast. The microphone signal was recorded for approximately 30 seconds. Once the data was recorded, the boat noise speaker was shifted to a different position (ex. 25 ft.) and the broadcasts and the recordings were repeated. For the five positions specified, there are 25 different combinations that were measured. Two additional tests were performed in which both speakers were placed at a horizontal distance 5 ft. from the microphone. In one test only the boat noise speaker broadcast and in the other test only the manatee speaker broadcast sound. These two tests emulate the boat or the manatee being place at an infinite distance.

It should be noted that for all 27 tests performed, it is assumed that the sound propagates according to a spherical spreading model, such that the sound pressure level will decay approximately 6 dB as the distance from the noise source is doubled.

Additionally, apart from the sound generated by the speakers, there also existed other background noise during the test that could not be removed. The background noise was primarily generated by traffic, birds, wind, airplanes, etc.

Conversion From Spherical to Mixed Spreading

The spherical transmission loss is given by

TLs = 20log10 ( Rs ) (6.22)

where TLs represents the spherical transmission loss and Rs represents the distance of the source from the microphone in spherical spreading model. The mixed transmission loss is given by

TLmm=15log10 ( R ) (6.23)

where TLm represents the mixed transmission loss and Rm represents the distance of the source from the microphone in mixed spreading model. Equating the transmission losses in Eq. (6.22) and Eq. (6.23), it can be given by

20log10 (Rs )= 15log 10 (Rm ) (6.24)

Solving for the mixed spreading distance in Eq. (6.24)

20 log (R ) 15 10 s Rm =10 (6.25)

However, since the distances are given in foot and the transmission loss is defined in meter, a conversion is necessary (1m~3.28ft.):

44 log (RR 3.28) (log− log 3.28) 3310ss 10 10 Rm ==10 10 44 44 −−log 3.28 (logRR ) (log ) 3310 10s 33 10 s Rm =⋅=⋅10 10 3.28 10 (6.26) 4 (logR ) 3 10 s Rm =⋅0.205 10

Eq. (6.26) will result in the equivalent distance in meter. If the distance is to be converted to ft., an additional conversion factor is required:

44 (logRR ) (log ) 3310s 10 s Rm =⋅3.28 0.205 ⋅ 10 = 0.673 ⋅ 10 (6.27)

Using Eq. (6.27) the spherical spreading ranges in ft. can be converted to mixed spreading ranges again in ft. The equivalent ranges for spherical spreading at 5, 25, 50,

75, and 100 ft then become 5.8, 49.2, 124.0, 212.8, and 312.6 ft., respectively for mixed spreading. The corresponding mixed spreading ranges in meter are 1.8, 15.0, 37.8, 64.9, and 95.3, respectively.

Simulation Results

The SNR of the acoustic superposed signal after bandpass filter, FIR-ALE, and

FALE cannot be estimated as well because the residue noise and manatee vocalizations cannot be separated from the processed signal and also because the temporal position of the vocalizations is not known in the measured data Therefore, the performance of the bandpass filter, FIR-ALE, and FALE will be shown only in time domain.

In the practical detection, a mechanism that controls the magnitude of the signal measured by the hydrophone should be used to adjust the magnitude of each recording to maintain them within a proper range after the bandpass filter is applied. As stated earlier, the performance of FIR-ALE and FALE with normalized step size is worse than that of

FIR-ALE and FALE with fixed step size. The strategy of normalized step size will provide small step size for the periods of manatee vocalizations and large step size for the rest periods when the SNR of the original manatee vocalizations shown in Figure 6-29 is high. Therefore, in the following simulations, the magnitude of each recording is adjusted and the fixed step size is used.

The original manatee vocalizations corrupted by background noise, the superposed signal after bandpass filtering, application of FIR-ALE, and application of FALE in time domain, when the location of manatee speaker is at 5 ft. and boat noise speaker is located at 100 ft, are shown in Figure 6-29(a-d), respectively. The cases with the location of boat

96 noise speaker (background noise) is at 100 ft. and manatee vocalizations at 25 ft., 50ft.,

75 ft., and 100 ft. are shown in Figure 6-30, Figure 6-31, Figure 6-32, and Figure 6-33, respectively. The cases with the location of background noise at 5 ft. and manatee vocalizations at 5 ft. and 25 ft. are shown in Figure 6-34 and Figure 6-35, respectively.

From Figure 6-35, the manatee vocalizations are completely masked by background noise when the location of manatee vocalizations is at 25 ft. and the background noise is located at 5 ft. For the case with the location of background noise at

5 ft. and manatee vocalizations at 50 ft (and further away) will not be shown because the manatee vocalizations after filtering are completely masked by the background noise.

(a) 1 0.5 0

Original signal 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpass filter Time (seconds) 0.5 (c)

After FIR-ALE -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE After -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-29. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 5 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

1.5 (a) 1 0.5 0 Original signal 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpassfilter Time (seconds) 0.5 (c)

After FIR-ALE After -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE After -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-30. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 25 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

2 (a)

Original signal 0 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpass filter Time (seconds) 0.5 (c)

After FIR-ALE After -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE After -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-31. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 50 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

3 (a) 2 1 0

Original signal -1 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpass filter Time (seconds) 0.5 (c)

After FIR-ALE -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-32. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 75 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

100

2 (a) 1.5 1 0.5 Original signal 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpass filter Time (seconds) 0.5 (c)

After FIR-ALE -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE After -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-33. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 100 ft and manatee vocalizations is located at 100 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR- ALE is applied and (d) after FALE is applied.

101

(a) 0.5

Original signal Original -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpass filter Time (seconds) 0.5 (c)

After FIR-ALE After -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE After -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-34. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 5 ft and manatee vocalizations is located at 5 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

102

(a) 0.5

Original signal -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (b)

-0.5 0 5 10 15 20 25 After bandpass filter Time (seconds) 0.5 (c)

After FIR-ALE After -0.5 0 5 10 15 20 25 Time (seconds) 0.5 (d)

0 After FALE -0.5 0 5 10 15 20 25 Time (seconds)

Figure 6-35. Performance of bandpass filter, FIR-ALE, and FALE for an acoustic superposition of manatee vocalizations and background noise when background noise is located at 5 ft and manatee vocalizations is located at 25 ft. (a) original signal, (b) after bandpass filter is applied, (c) after FIR-ALE is applied and (d) after FALE is applied.

CHAPTER 7 PERFORMANCE COMPARISON BETWEEN FIR-ALE AND FALE

The comparisons between FIR-ALE and FALE based on real recordings of manatee vocalizations have been shown in Chapter 6. In this chapter, four aspects, namely computational complexity, stability, convergence rate and tracking ability, are selected as the evaluation criteria to compare the performance of FIR-ALE and FALE using simulations. The advantage and disadvantage of FIR-ALE and FALE are discussed in this chapter.

Computational Complexity

An important aspect for real-time calculations is the computational requirements of the algorithm. As stated in Chapter 3, many algorithms are not selected as potential noise reduction algorithms for the manatee problem mainly because of their computational complexity. The number of operations per iteration for FIR-ALE and FALE are computed below, respectively. The typical sampling frequency of the manatee vocalizations observed by a hydrophone is 48 kHz.

FIR-ALE

In order to make the computation complexity clear, the necessary computations of

FIR-ALE introduced in Chapter 4 are briefly described here again.

akii (+= 1) ak ( ) +µ ekxk ( )′ ( − i ) i = 0, 1, " , L − 1 (7.1)

LL−−11 ˆ ′ sk()=−=−∆−∑∑ aii () kx ( k i ) a ()( kxk i ) (7.2) ii==00

ek()= xk ()− skˆ () (7.3)

103 104

th where aki ( ) represent the i weight of the adaptive filter at iteration k , L and µ represents the order and step size of the adaptive filter, respectively, x (k ) is the observed signal and x′ (k ) is the delayed version of x (k ) , sˆ represents the estimate of narrowband component s in the observed signal, and e is the error of the adaptive filter. The requirements of multiplications and additions per iteration are listed in the Table 7-1.

From the table, the number of multiplications and additions are 2L + 1 and 2L , respectively. Since the sampling frequency of the manatee vocalizations is 48 kHz, the number of multiplications and additions of the FIR-ALE in one second are

96000L + 48000 and 96000L , respectively.

Table 7-1. Computational complexity of FIR-ALE. Operation No. of Multiplications No. of Additions akii(1)()+= ak +µ ekxk()()′ − i L +1 L L−1 ˆ ′ sk()=−∑ axi ( k i ) L L −1 i=0 ek()=− xk () skˆ () 0 1 Total 21L + 2L

FALE

The necessary computations of the FALE algorithm introduced in Chapter 4 are also briefly described here again.

xk′()= β skˆ (−−∆+ 1 ) (1 −β )( xk −−∆ 1 ) (7.4)

akii (+= 1) ak ( ) +µ ekxk ( )′ ( − i ) i = 0, 1, " , L − 1 (7.5)

L−1 ˆ ′ sk()= ∑ axi ( k− i ) (7.6) i=0

ek()= xk ()− skˆ () (7.7)

105

The variable definitions of all the parameters for FALE are the same as those of FIR-

ALE. β represents the feedback constant of FLAE. The number of multiplications and additions per iteration are listed in the Table 7-2. The number of multiplications and additions of the FALE in one second are 96000L + 144000 and 96000L + 48000 , respectively.

Table 7-2. Computational complexity of FALE. Operation No. of Multiplications No. of Additions xk′()=−−∆+−−−∆β skˆ ( 1 ) (1β )( xk 1 ) 2 1 ′ akii(1)()+= ak +µ ekxk()() − i L +1 L L−1 ˆ ′ sk()=−∑ axi ( k i ) L L −1 i=0 ek()=− xk () skˆ () 0 1 Total 23L + 21L +

Usually, a DSP only requires several clock cycles to complete one multiplication or addition. In the current DSP market, the frequency of a general microprocessor is between 10 MHz to 1 GHz. In the simulations shown in Chapter 6, the order of the adaptive filter is set to 20. For example, one floating point multiplication of a microprocessor with a pipeline structure only needs 2 clock cycles and one addition needs 3 clock cycles. Therefore, FIR-ALE needs

clock cycle per second=(96000LLe+ 48000)×+ 2 96000 ×= 3 9.696 6 (7.8)

That is to say, the algorithm can be implemented in real time only when the clock cycle of the microprocessor is less than 103.1 ns or the frequency of the microprocessor is larger than 9.696 MHz. Similarly, it is easy to find that feedback ALE can be implemented in real time only when the frequency of the microprocessor is larger than

10.032 MHz. Generally, a microprocessor with frequency 40 MHz is fast enough to implement the FIR-ALE or FALE in real time.

106

Stability

The required condition for a stable system is that all poles of the filter are inside the unit circle. The poles of the FIR-ALE are at the origin all the time; therefore it is

unconditionally stable. If the input to the FIR-ALE is a sinusoid with frequency ω0 corrupted by white noise, the narrowband output of FIR-ALE will be the estimate of the input sinusoidal signal. The transfer function between the input and narrowband output of FIR-ALE, F (ω ) (shorthand notation of Fe (jω ) ), is given by

FeF()ω = −∆jω ()ω (7.9) and meets the constraint given by

−∆jω0 0()1< eFω0 < (7.10) where F(ω ) represents the FIR block in Figure 4-4. The transfer function between the input and narrowband output of the FALE is given by

Szˆ() (1− β ) z−∆ Fz () Hz()== (7.11) X ()zzFz 1− β −∆ () where Szˆ(), X (z ) represent the Z transform of skˆ() and x (k ) , respectively.

L−1 −k −∆ Fz()= ∑ azk is the z-transform of the weights of the adaptive FIR filter. zFz ( ) k=0 represents the transfer function of the FIR filter with the line delay included. Therefore, the poles of Hz ( ) satisfy

1 zFz−∆ ()= (7.12) β

From the Eq. (7.9) and (7.10), F()ω0 is less than 1 on the unit circle and increases to infinity at the origin because the poles of the FIR structure are all at the origin all the

107 time, since 0<<β 1, 1/β > 1. Therefore, the roots of the Eq. (7.12) must lie within the unit circle (Chang, 1993). The above analysis shows that the FALE is stable under the assumption that Eq. (7.10) is met all the time.

Convergence Rate and Tracking Ability

The convergence rate and tracking ability of an adaptive filter are important factors for tracking a nonstationary signal. The passband formed by the FALE is going to be narrower as the feedback constant β is increased. The FALE algorithm has the ability to generate a narrower passband (sharper resonance) than an equivalent order FIR-ALE algorithm due to the addition of poles within the filter. However, the poles of the FALE make its convergence rate slower than FIR-ALE (see Figure 7-1) and affect the general numerical sensitivity of the filter. In addition to moving the zero positions toward the unit circle, which makes the bandwidth narrower, feedback introduces poles at the same time. Poles close to the unit circle make the filter very sensitive to perturbations to the filter weights. Therefore, the FALE requires a smaller step size than FIR-ALE to keep the filter stable. However, the feedback of the FALE makes its convergence rate somewhat slower than FIR-ALE with same step size. Therefore, it is difficult for FALE to achieve good stability margin and faster convergence at the same time. The benefits of

FALE are obtained at the expense of the robustness of the system and the convergence rate.

Chang suggested that Fw()0 may have values greater than one occasionally, especially when the step size is relatively large (Chang, 1993). Therefore, the system may be unstable even with the same step size as that of FIR-ALE. That is to say, the smaller the feedback constant β , the smaller the probability of the system going

108

unstable, by the values of Fw()0 larger than one. Therefore, the step size and feedback constant β of FALE should be kept small to avoid instability. On the other hand, a large step size and feedback constant β are required to obtain fast convergence and better tracking ability. Therefore, there exists a tradeoff between the convergence rate and stability.

Chang (1993) proposed a mechanism of using an automatically increasing feedback constant β , called exponential β . The value of the exponential β is computed recursively by

βkk+∞1 = βγ+− β(1 γ ) (7.13) where 0<<γ 1 is the constant that controls the growth time constant, β is the feedback

constant, and β∞ represents the final value of β . Gain growth trajectories of FALE with constant β , FALE with exponential β , and FIR-ALE for extracting a single sinusoid from white noise are shown in Figure 7-1. The simulations show that the FALE with exponential feedback has the best convergence rate among these three algorithms, which not only provides fastest convergence but also best filter gain among these three algorithms. The FALE with constant β has good filter gain at the expense of slow convergence. The filter gain is defined as the magnitude ratio of the narrowband output and primary input of the adaptive filter. Gain growth mentioned in Figure 7-1 represents the change of the filter gain during adaptation. FALE with exponential β can provide a faster convergence rate than the FALE with constant β at the expense of increasing the computational effort. It is difficult to implement FALE with exponential β for the

109 manatee problem because β should be exponentially increased only during the manatee call period and kept low for others.

From Figure 7-1, the FALE gain exhibits larger fluctuations than the FIR-ALE does under same conditions, which occurs due to the feedback structure. The characteristic of the FALE makes its stability margin smaller, thus it is easy to be unstable due to large perturbation. As stated earlier, a large step size is used to obtain fast convergence rates at the expense of large misadjustment and increasing the probability of divergence. Therefore, it is very important to select a proper step size for

FALE, which not only makes FALE track the nonstationary signal but also makes the system remain stable. That is to say, the step size should be the minimum value that can track the nonstationary signal. Marshall suggested that if FALE is able to track the nonstationary signal, increasing the amount of feedback β can improve the accuracy of its instantaneous frequency estimate (Marshall, 1994). However, if the FALE cannot track the nonstationary signal, it will cause greater output error than does the FIR-ALE.

FALE with constant β FALE with exponential 1.2 β FIR-ALE

0.8

0.6 Filter gainFilter

0.4

0.2

0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Iteration number Figure 7-1. Gain growth trajectories of FALE with fixed β , FALE with exponential β , and FIR structure ALE for extracting a single sinusoid from white noise.

110

Advantage and Disadvantage of FIR-ALE and FALE

The simulation results shown in Chapter 6 indicate that the performance of FALE is better than that of FIR-ALE for most manatee vocalizations. The improvement of

FALE over FIR-ALE becomes large when the SNR of the original manatee vocalizations increases. As the narrowband output of FALE is re-filtered by the feedback, the noise component is progressively reduced. The result shown in Figure 7-1 suggests that the filter gain of FALE is better than that of FIR-ALE at the expense of larger fluctuations.

As stated earlier, the normalized LMS algorithm is not suitable to manatee problem and the step size of FIR-ALE and FALE are set to 0.1 and 1, respectively. A large step size is used for FALE to improve the tracking ability at the expense of the robustness.

The stability margin of FALE with step size of 1 is much smaller than that of FIR-ALE with step size of 0.1. The tracking ability of FALE depends on the step size and feedback constant. The tracking ability of FALE is improved when the step size is increased or feedback constant is decreased or both. Therefore, the tracking ability of FALE is worse than that of FIR-ALE when the step size is same for them. In general, the step size of

FALE should be smaller than that of FIR-ALE in order to achieve stability. However, the smaller step size of FALE will degrade its tracking ability. There exists a tradeoff between the stability margin and the performance.

The lower bound for overall performance of FIR-ALE and FALE as a function of the SNR of the original manatee call for different step sizes is shown in Figure 7-2 and

Figure 7-3, respectively. From Figure 7-2, the performance of FIR-ALE degrades as the step size increases because of the misadjustment. However, the performance of FALE is improved as the step size increases, when the SNR of original manatee vocalizations is lower than -6 dB. As stated earlier, a smaller step size can be used to reduce the

111 misadjustment and a large step size can be used to improve the tracking ability. That is to say, if the step size is set to large, the benefit obtained by good tracking ability is larger than the loss caused by a large misadjustment, when the SNR of original manatee vocalizations is less than -6 dB.

25 mu=0.1 mu=0.2 20 mu=0.3 mu=0.4 15 mu=0.5 mu=0.6 10 mu=0.7 5 mu=0.8 mu=0.9 0 mu=1.0

-5 SNR FIR-ALE (dB) after -10

-15

-20

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori

Figure 7-2. Lower bound for overall performance of FIR-ALE as a function of the SNR of the original manatee call for different step sizes.

40 mu=0.1 mu=0.2 30 mu=0.3 mu=0.4 mu=0.5 20 mu=0.6 mu=0.7 mu=0.8 10 mu=0.9 mu=1.0 0 SNR FALE (dB) after

-10

-20

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori

Figure 7-3 Lower bound for overall performance of FALE as a function of the SNR of the original manatee call for different step sizes.

112

The improvement of FALE over FIR-ALE is shown in Figure 7-4 when the step size of FIR_ALE and FALE are both set to the same value. From this figure, if the step size is set to 0.1 for a large stability margin, the performance of FALE is worse than that of FIR-ALE when the SNR of the original manatee vocalizations are lower than -10 dB.

The improvement of FALE over FIR-ALE becomes large as the step size increases.

However, the performance improvements obtained by FALE is at the expense of the stability margin.

20 mu=0.1 mu=0.2 mu=0.3 15 mu=0.4 mu=0.5 mu=0.6 10 mu=0.7 mu=0.8 mu=0.9 5 mu=1.0 Gain (dB) Gain

-5

-10 -25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori Figure 7-4. Improvement of FALE over FIR-ALE for different step sizes.

From the previous discussion, the performance of FIR-ALE and FALE depends on the step size, delay, order, and feedback constant. The value of the step size is also determined by the magnitude of the input signal of the adaptive filter. In order to achieve optimal filtering results for a given vocalization, each vocalization needs a different step size, order, delay, and feedback constant. Clearly, there is a trade off between these parameters since no two vocalizations are identical. The selection of parameters used in this dissertation has not been optimized to span the full range of differing vocalizations.

Optimization of the parameters is left as future work.

CHAPTER 8 DETECTION RANGE ESTIMATION

One aspect of the feasibility of an acoustic-based detection system relies upon the distance over which a manatee vocalization is detectable. In this chapter, the improvements the detection range of FIR-ALE over a bandpass filter, FALE over a bandpass filter, and FALE over FIR_ALE are estimated according to the lower bound and upper bound of the performance of a bandpass filter, FIR-ALE, and FALE obtained in Chapter 6. The improved detection ranges of a bandpass filter, FIR-ALE, and FALE are estimated according to the spreading model obtained by Phillips et al. (2006) as well.

Theoretical Development

The following derivation of the detection range was presented in the work by

Phillips et al. (2006) and is reviewed here. Manatee detection systems based upon acoustically detecting vocalizations are essentially passive sonar systems. The relevant equations are applicable to this problem and are detailed in the work by Caruthers (1977) and Ross (1976). These equations are now reviewed. The detection threshold ( DT ) of a passive sonar system is the minimum signal strength above the ambient noise level ( NL ) required to detect the signal. The Sound Pressure Level (SPL) received by the hydrophone is the source level ( SL ), measured at 1 m, minus any transmission loss (TL ) that may occur. The signal excess ( SE ) is the amount by which the detection threshold is exceeded (Eq. (8.1)), where DI is the directivity index of the system and AG is the array gain when multiple hydrophones are used. If the signal excess is greater than or

113 114 equal to zero, the signal can be detected by the passive sonar system, and as the signal excess increases the probability of detection increases.

SE= SL−− TL NL + DI + AG − DT (8.1)

When there is no SE , and SL and NL are known, equation 1 can be solved for the maximum allowable transmission loss (Eq. (8.2)). The maximum allowable transmission loss is traditionally referred to as the figure of merit ( FOM ).

FOM= SL−++ NL DI AG − DT (8.2)

For the purpose of this study a single hydrophone (omni-directional) system is considered, and the manatee vocalizations are assumed omni-directional. These assumptions reduce the array gain and directivity index of Eq. (8.2)to zero.

FOM= SL−− NL DT (8.3)

In addition to ambient background noise, this study also considers the effects of boat noise. To compensate for noise from boats the ambient noise level is considered to be the maximum of the ambient noise level and the received boat noise ( RN ).

FOM=− SLmax( NL , RN) − DT (8.4)

The received boat noise is the source level of the boat ( SLB ) with any transmission

losses (TLB ) subtracted. The maximum allowable transmission loss for a manatee

vocalization is shown in Eq. (8.5), where SLM is the source level of the manatee vocalization.

FOM=− SLMBBmax( NL , SL −− TL) DT (8.5)

The transmission losses due to acoustic spreading of the manatee vocalizations and boat noise are best approximated by a mixed spreading model (Phillips et al., 2006). The

115 mixed spreading model is an intermediate model between spherical and cylindrical spreading. The transmission loss due to mixed spreading is,

TL=15⋅≥ log( R) R 1 (8.6) where R (meters) is the distance from the source with reference to 1 m (Coates, 1989).

To obtain the sonar equation in terms of the manatee detection distance ( RM ) and the

boat distance ( RB ), Eq. (8.6) is substituted into Eq. (8.5) for the transmission loss of the boat noise and the figure of merit.

15⋅=− log()RMMSL max( NL , SL B −⋅− 15 log( R B)) DT (8.7)

Rearranging Eq. (8.7), the sonar equation yields the maximum distance a manatee is detectable and is given by,

⎛⎞ ⎛⎞SL−−⋅−max⎜⎟ NL , SL 15 log ( R) DT R =10 ^ ⎜⎟MBB⎝⎠ (8.8) M ⎜⎟ ⎝⎠15

The maximum distance in which a manatee is detectable ( RM ) is dependent on the source

level of the manatee vocalization ( SLM ), the ambient noise level ( NL ), the source level

of the boat ( SLB ), the distance of the boat from the hydrophone ( RB ), the type of acoustic spreading model chosen (mixed-spreading), and the system detection threshold

( DT ).

Estimation of Improved Detection Range

Firstly, the improvement of detection range of the system enhanced by FIR-ALE over bandpass filter, FALE over bandpass filter, and FALE over FIR-ALE is estimated.

The lower bound and upper bound of the performance of these three algorithms will give a bound for the estimated detection range. These estimations are based on an assumption

116 that the distortion on the frequency structure of manatee vocalizations caused by ALE is small and ignored. If the distortion is taken into account, the detection range should be less than the theoretical results obtained below. Secondly, the improved detection ranges of the system enhanced by bandpass filter, FIR-ALE, and FALE are estimated according to the Eq. (8.8).

Supposed that two manatees and one detection device shown in Figure 8-1 are in

their habitat, where R1 represents the maximum distance that the manatee is detectable

only using a bandpass filter and R2 represents the maximum distance that the manatee is detectable using a bandpass filter and ALE algorithm (FIR-ALE or FALE). Several assumptions are made as follow.

• The background noise received by the hydrophone is the same for the manatees located in either position.

• The source pressure levels of these two manatee vocalizations are the same.

• The model of transmission loss in their same habitat is the same.

• Single hydrophone system is considered.

• The manatee vocalizations are assumed non-directional.

Figure 8-1. Illustration of the manatee detection.

117

The lower bound and upper bound of the performance of FIR-ALE and FALE has been found and shown in Figure 6-26 when the SNR of the original manatee vocalizations varies from -25 dB to 0 dB. In order to compare the detection range of

FIR-ALE and FALE with that of a bandpass filter, the lower bound performance of FIR-

ALE and FALE versus the lower bound performance of bandpass filter is shown in

Figure 8-2. An example is used to show how to calculate the lower bound for the improvement of the detection range of the enhanced by FIR-ALE over a bandpass filter.

If the system only operates with a bandpass filter and the lowest SNR BPF (lower bound) that the system can detect a vocalization is 0 dB, then after FIR-ALE is applied the

lowest SNR BPF of a vocalization that can be detected will be improved to -8.34 dB.

Therefore, the improvement in terms of SNR obtained by FIR-ALE over bandpass filter is 8.34 dB. Similarly, the improvement obtained by FALE over bandpass filter is about

10.41 dB. Therefore, the improvement obtained by FALE over FIR-ALE is 2.07 dB.

After FIR-ALE (Lower bound) 30 After FALE (Lower bound)

0 SNR after filtering (dB)

-10

-10.41 -8.34 -20 -20 -15 -10______-5 0 5 Average of SNR (Lower bound in dB) BPF

Figure 8-2. Lower bound of the overall performance comparison between the bandpass filter, FIR-ALE, and FALE as a function of the SNR of the manatee vocalizations after bandpass filtering

118

From the Eqn. (8.8), we have

⎛⎞ ⎛⎞SL−−⋅−max⎜⎟ BL , SL 15 log ( R) DT R =10 ^ ⎜⎟MBB11⎝⎠ (8.9) 1 ⎜⎟ ⎝⎠15

⎛⎞ ⎛⎞SL−−⋅−max⎜⎟ BL , SL 15 log ( R) DT R =10 ^ ⎜⎟MBB22⎝⎠ (8.10) 2 ⎜⎟ ⎝⎠15

According to assumptions, SLM 12= SLM and background noise is also same for these two manatee vocalizations. The threshold value is the minimum SNR of the manatee call

received by hydrophone that is detectable. Therefore, DT1 = 0 dB and DT2 =−8.34 dB .

The ratio R21/ R is given by

08.34+ () 15 RR21/10= (8.11)

8.34/15 R211==10RR 3.6 (8.12)

For this example, Eq. (8.12) suggests that the detection distance of the system enhanced by FIR-ALE is 3.6 times of the one only using a bandpass filter. Similarly, the detection distance of the system enhanced by FALE is 4.9 times of the one only using a bandpass filter.

In order to calculate the improvement of the detection range of FIR-ALE and

FALE compares to a bandpass filter for the SNR of manatee vocalizations after bandpass filter is applied, a polynomial is used to fit the data in Figure 8-2. The curve fits for the performance of FIR-ALE and FALE are shown in Figure 8-3. In order to reduce the estimation error of the curve at low SNR, a high order polynomial is used to fit these data. The polynomial equation for the performance of FIR-ALE and FALE are given by

Eq. (8.13) and Eq. (8.14), respectively.

119

yxxx=×4.498 10−−−65 +× 2.491 10 44 +× 1.371 10 33 1 (8.13) −× 4.454 10−22xx + 1.651 + 16.642

yxxxx=−3.112 × 10−−−66 − 1.252 × 10 45 − 9.764 × 10 44 + 7.724 × 10 − 33 2 (8.14) +× 4.283 10−32xx + 1.424 + 23.180 where x represents the lower bound of the SNR of manatee vocalizations after bandpass

filter is applied, and y1 , and y2 represent estimates for the lower bound of the SNR of manatee vocalizations after FIR-ALE and FALE is applied, respectively.

According to the Eq. (8.10), the relationship between the ratio of R2/R1 and the

lowest SNR BPF (lower bound) that the system can detect a vocalization by only using a bandpass filter is shown in Figure 8-4. The improvements of FIR-ALE over bandpass filter, FALE over bandpass filter, and FALE over FIR-ALE become larger as the

SNR BPF increases. There are no improvements for FIR-ALE and FALE when SNR BPF is as low as -18 dB.

After FIR-ALE 30 After FALE

0 SNR after filtering (dB) -10

-20

-20 -15 -10 ______-5 0 5 Average of SNR (dB) BPF

Figure 8-3. Curve fittings for the performance of FIR-ALE and FALE.

120

12 Improvement FIR-ALE over bandpass filter Improvement FALE over bandpass filter 10 Improvement FALE over FIR-ALE

8 1

/R 6 2 R

0 -15 -10 -5 0 5 Lowest SNR (lower bound) that the system BPF can detect a vocalization by only using a bandpass filter

Figure 8-4. Lower bound for the relationship between the ratio of R2/R1 and the lowest

SNR BPF (lower bound) that the system can detect a vocalization by only using a bandpass filter.

The upper bound is investigated now. The curve fit for the upper bound of the performance of FIR-ALE and FALE is shown in Figure 8-5. The upper bound for the

relationship between the ratio of R2/R1 and the lowest SNR BPF (lower bound) that the system can detect a vocalization by only using a bandpass filter is shown in Figure 8-6.

The overall comparison between the lower bound and upper bound of FIR-ALE and

FALE are shown in Figure 8-7. The results shown in this figure provide a relative tight lower bound and upper bound. The preceding results indicate that as the SNR of the manatee vocalization is reduced, so does the performance of the adaptive filters, compared to the performance of a bandpass filter. The improvement of the FIR-ALE and

FALE algorithms over a bandpass filter depends on the lowest SNR BPF (lower bound) that the system can detect a vocalization by only using a bandpass filter.

121

After bandpass filter 30 After FIR-ALE After FALE

10 SNR after (dB) filtering

-25 -20 -15 ______-10 -5 0 Average of SNR (dB) ori

Figure 8-5. Curve fitting for upper bound of the performance of FIR-ALE and FALE

10 Improvement FIR-ALE over bandpass filter 9 Improvement FALE over bandpass filter Improvement FALE over FIR-ALE 8

6 1

/R 5 2 R 4

0 -15 -10 -5 0 5 Lowest SNR (lower bound) that the system BPF can detect a vocalization by only using a bandpass filter (dB)

Figure 8-6. Upper bound for the relationship between the ratio of R2/R1 and the lowest

SNRBPF (lower bound) that the system can detect a vocalization by only using a bandpass filter.

122

10 Lower bound for FIR-ALE 9 Upper bound for FIR-ALE Lower bound for FALE 8 Upper bound for FALE

6 1

/R 5 2 R 4

0 -15 -10 -5 0 5

Lowest SNRBPF (lower bound) that the system can detect a vocalization by only using a bandpass filter (dB)

Figure 8-7. Overall comparison between the lower bound and upper bound of FIR-ALE and FALE.

Estimation of the Improved Detection Range

SPL of Manatee Vocalizations and Background Noise

The magnitude of the environmental noise and manatee vocalizations, as well as the acoustic spreading properties of the habitat, are required to estimate the detection range of a vocalizing manatee. Nowacek et al. (2003) measured the average received levels of the peak frequency to be approximately 100 dB (re 1µPa) and approximated the source levels to be within 6 to 15 dB of the received levels. The recordings were made with a hydrophone located approximately 20 m away from a group of about 50 manatees.

By using a hydrophone array, position estimation techniques, and the received sound pressure levels, the mean source level of the manatee vocalizations was approximated to be 112 dB @ 1m (Phillips et al., 2004). In their paper, cylindrical spreading of the acoustic pressure propagation through the water is assumed to estimate the source level. Recently, it was determined that a mixed spreading model is more appropriate (Phillips et al., 2005). If the mixed spreading model that is an intermediate

123 model between spherical and cylindrical spreading is used in their analysis, the manatee source levels will be close to 118 dB @ 1m (Phillips et al., 2006).

Miksis-Olds et al. (2004) analyzed the relationship between ambient noise levels and manatee habitat use. They found that the high-use manatee habitats have higher transmission losses and lower ambient noise in the early morning and later afternoon hours compared to low-use habitats.

The noise generated by boating traffic has been measured between 129 and 169 dB

@ 1m, with an overall SPL of approximately 140 dB (Phillips et al., 2006). At frequencies above 1.2 kHz, 90% of the measured boat traffic has a maximum noise floor less than 125 dB. Schevill and Watkins (1965) found that the manatees calls were not particularly loud and many of them were only 10 ~ 12 dB above background noise at distances of 3~4 m (Schevill and Watkins, 1965). The ambient noise measured by

Phillips et al. varies between 70 dB and 105 dB (Phillips et al., 2006).

Although manatee vocalizations levels and background noise have some variability, the average value (112 dB @ 1m) of manatee vocalizations, (125 dB @ 1m) boat noise, and (70, 80, 90 dB, and 100 dB @ 1m) ambient noise after the bandpass filter is applied will be used to estimate the detection range. The detection range of the system enhanced by a bandpass filter, FIR-ALE, and FALE are estimated in the next three sections, respectively.

Estimation of Detection Range (bandpass filter)

The maximum detection range of the device can be estimated with respect to the detection threshold by using Eq. (8.8) after knowing the source level of the manatee vocalizations, boat noise, and ambient noise. The maximum manatee detection ranges

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for a background noise level ( NL ) of 70 dB and a boat source level ( SLB ) of 125 dB only using a bandpass filter is shown in Figure 8-8. Similar detection range results are plotted

for a NL =80 dB and SLB =125 dB as shown in Figure 8-9.

Each of the three graphs in Figure 8-8 and Figure 8-9, contain the same information presented in a slightly different manner. For example if the reader peruses the lower right hand graph of Figure 8-8, for a detection threshold of 3 dB, it is evident that the detection range is ~43 m when the boat is located 500 m away from the hydrophone. If the boat moves closer and is located 200 m from the hydrophone, the manatee detection range drops to ~17 m. If the boat moves even closer and is located less than 11 m from the hydrophone, the boat noise levels have exceeded the detection threshold (3 dB) required to detect the manatee.

As the ambient background noise levels increase from 70 dB, the results presented in Figure 8-8 will not change until ~84.5 dB for a boat operating within 500 m of the hydrophone and a manatee source level of 112 dB. With ambient background noise levels less than 84.5 dB, the limiting factor in the manatee detection distance is the boat noise, for a boat cruising within 500 m of the manatee. If the ambient background noise levels are increased to 90 dB (see Figure 8-11), the detection range is governed by the ambient noise until the boat is located closer than ~216 m from the hydrophone. Within the range <216 m, the boat noise limits the detection range, while if the boat is further than 216 m, the detection range is limited by the ambient noise.

For a manatee source level of 112 dB, in all of the cases the hydrophone is saturated by engine and propeller noise when the boat is closer than 5 to 10 m, depending on the detection threshold.

125

Estimation of Detection Range (FIR-ALE)

Once the FIR-ALE are applied for a NL =70 dB and SLB =125 the detection range results are shown in Figure 8-12. Similar detection range results are plotted for a NL =80

dB and SLB =125 dB as shown in Figure 8-13.

Likewise, if the reader peruses the lower right hand graph of Figure 8-12, for a detection threshold of 3 dB, it is evident that the detection range is increased to ~198 m when the boat is located 500 m away from the hydrophone. The detection range obtain by FIR-ALE is 4.6 times as that obtained by a bandpass filter when the threshold is set to

3 dB, which conforms to results shown in Figure 8-7. If the boat moves closer and is located 200 m from the hydrophone, the manatee detection range drops to ~79 m. If the boat moves even closer and is located less than 2.5 m from the hydrophone, the boat noise levels have exceeded the detection threshold (3 dB) required to detect the manatee.

As the ambient background noise levels increase from 70 dB, the results presented in Figure 8-10 will not change until ~84.5 dB for a boat operating within 500 m of the hydrophone and a manatee source level of 112 dB, which is same as the system enhanced

by FALE or a bandpass filter because it depends on the SPL of boat noise ( SLB ), distance

of boat noise ( RB ), and spreading model (see Eq.(8.8)).

Estimation of Detection Range (FALE)

Once the bandpass filter and FALE are applied for a NL =70 dB and SLB =125 dB the detection range results are shown in Figure 8-16. Similar detection range results are

plotted for a NL =80 dB and SLB =125 dB as shown in Figure 8-17.

Likewise, if the reader peruses the lower right hand graph of Figure 8-16, for a detection threshold of 3 dB, it is evident that the detection range is increased to ~290 m

126 when the boat is located 500 m away from the hydrophone. The detection range obtained by FALE is 6.7 times as that obtained by a bandpass filter when the threshold is set to 3 dB, which also conforms to results shown in Figure 8-7. If the boat moves closer and is located 200 m from the hydrophone, the manatee detection range drops to ~116 m. If the boat moves even closer and is located less than 1.5 m from the hydrophone, the boat noise levels have exceeded the detection threshold (3 dB) required to detect the manatee.

From these figures and discussions, the detection range is largely improved when an adaptive filter is implemented. The improvements of FIR-ALE and FALE become larger when the detection threshold increases.

500

140 9 . 2 2 . 0 8 400 1 8 .4 9 2 .5 3 7 120 300 160 .8 8 5 200 140 .1 44 100 Boat Distance (m) 4.7 120 100 1

100 0 -5 0 5 80 Detection Threshold (dB) 80

60 60 80 DT=0dB 40 DT=3dB

Manatee Detection Distance (m) 60 DT=6dB 20 40

0 40 500 -4 400 20 -2 20 0 300 2 200 Manatee Detection Distance (m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-8. Maximum manatee detection ranges at NL =70 dB and SLB =125 dB only using a bandpass filter.

127

500

140 9 . 2 2 . 0 8 400 1 8 .4 9 2 .5 3 7 120 300 160 .8 8 5 200 140 .1 44 100 Boat Distance (m) 4.7 120 100 1

100 0 -5 0 5 80 Detection Threshold (dB) 80

60 60 80 DT=0dB 40 DT=3dB

Manatee Detection Distance (m) 60 DT=6dB 20 40

0 40 500 -4 400 20 -2 20 0 300 2 200 ManateeDetection Distance (m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-9. Maximum manatee detection ranges at NL =80 dB and SLB =125 dB only using a bandpass filter.

500

60 12.8 32

400 57.6 51.2

300 70 6

. 50 8 . 5

4 2

4 .2 200 9 60 .4 1 38 Boat Distance (m) 100 8 50 40 12. 6.4

0 40 -5 0 5 Detection Threshold (dB)

30 30

50 20 DT=0dB DT=3dB

Manatee Detection Distance (m) 40 20 DT=6dB 10 30 0 500 20 -4 10 400 -2 0 300 10 200

2 ManateeDetection Distance (m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-10. Maximum manatee detection ranges at NL =90 dB and SLB =125 dB only using a bandpass filter.

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500 5.6 7 4.2 400 12

. 8.4

300 2.8

15 11.2

10 200 12.6 Boat Distance (m) 100

10 7 54.6.2 8 0 12.4.8 -5 0 5 Detection Threshold (dB)

6 5 10 DT=0dB DT=3dB 8 Manatee Detection Distance(m) DT=6dB 4 6 0 500 4 -4 400 2 -2 0 300 2 2 200 Manatee Detection Distance(m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-11. Maximum manatee detection ranges at NL =100 dB and SLB =125 dB only using a bandpass filter.

500 5 .9 3. 2 7 24 1 400 2 8. 300 0 8 2 8. 300 13 400

350 200 .1 250 104

Boat Distance (m) 69.4 300 100 34.7 250 200 0 -5 0 5 Detection Threshold (dB) 200

150 150 300 DT=0dB 100 250 DT=3dB Manatee Detection Distance (m) DT=6dB 50 100 200

0 150 500 -4 400 50 100 -2 300 0 50 2 200 Manatee Detection Distance (m) 4 100 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-12. Maximum manatee detection ranges at NL =70 dB and SLB =125 dB after FIR-ALE is applied.

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500 5 .9 3. 7 242 1 400 2 8. 300 0 8 2 8. 300 13 400

350 200 .1 250 104

Boat Distance (m) 69.4 300 100 34.7 250 200 0 -5 0 5 Detection Threshold (dB) 200

150 150 300 DT=0dB 100 250 DT=3dB Manatee Detection Distance (m) DT=6dB 50 100 200

0 150 500 -4 400 50 100 -2 300 0 50 2 200 Manatee Detection Distance (m) 4 100 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-13. Maximum manatee detection ranges at NL =80 dB and SLB =125 dB after FIR-ALE is applied.

500 90 75 140 400

300 160 120

5 3 200 1 20 140 1 105

Boat Distance(m) 75 120 100 100 60 45 30 15 100 0 -5 0 5 80 Detection Threshold (dB) 80

60 60 150 DT=0dB 40 DT=3dB Manatee Detection Distance (m) DT=6dB 20 40 100 0 500 -4 400 20 50 -2 0 300 200

2 Manatee Detection Distance (m) 4 100 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-14. Maximum manatee detection ranges at NL =90 dB and SLB =125 dB after FIR-ALE is applied.

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500

30 19.8

400 29.7 16.5

300 26.4 40 25 35 200 Boat Distance (m) 30 100 .1 3 20 2 19.8 16.513.2 9..69 25 0 3.3 6 -5 0 5 Detection Threshold (dB) 20 15 15 40 DT=0dB 10 DT=3dB Manatee Detection Distance (m) 10 30 DT=6dB 5

0 20 500 -4 5 400 -2 10 0 300 2 200 Manatee Detection Distance (m) 4 100 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-15. Maximum manatee detection ranges at NL =100 dB and SLB =125 dB after FIR-ALE is applied.

500

3.2 400 34 .3 00 7.4 400 3 25

5 1.6 300 14. 17 500 350 2

450 200 8.7 300 12 400 Boat Distance (m) 100 85.8 350 42.9

300 250 0 -5 0 5 Detection Threshold (dB) 250 200 200 400 150 DT=0dB 150 DT=3dB

Manatee Detection Distance (m) Distance Detection Manatee 100 300 DT=6dB 50 100 0 200 500 -4 400 -2 50 100 0 300 200

2 Manatee Detection Distance (m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-16. Maximum manatee detection ranges at NL =70 dB and SLB =125 dB after FALE is applied.

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500

3.2 400 34 .3 00 7.4 400 3 25

5 1.6 300 14. 17 500 350 2

450 200 8.7 300 12 400 Boat Distance (m) 100 85.8 350 42.9

300 250 0 -5 0 5 Detection Threshold (dB) 250 200 200 400 150 DT=0dB 150 DT=3dB

Manatee Detection Distance (m) 100 300 DT=6dB 50 100 0 200 500 -4 400 -2 50 100 0 300 200

2 Manatee Detection Distance (m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-17. Maximum manatee detection ranges at NL =80 dB and SLB =125 dB after FALE is applied.

500 180

400 1

1 160 300

200 5 5 . .

6 9

6 2 140 1 1 180 200 148

160 Boat Distance (m) 111 92.5 74 100 120 55.5 140 37 18.5 120 0 -5 0 5 100 Detection Threshold (dB) 100

80 80 250 60 DT=0dB DT=3dB

Manatee Detection Distance (m) Distance Detection Manatee 40 200 60 DT=6dB 20 150 0 40 500 100 -4 400 -2 20 0 300 50 200 2 Manatee Detection Distance (m) 100 4 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-18. Maximum manatee detection ranges at NL =90 dB and SLB =125 dB after FALE is applied.

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500 36 32 28 400 35 24 300 50

45 30 200

40 Boat Distance (m) 100 35 25 32 22840 6 4 1 12 8 30 0 -5 0 5 Detection Threshold (dB) 25 20

20 50 15 15 DT=0dB DT=3dB

Manatee Detection Distance (m) 10 40 DT=6dB 5 10 30 0 500 20 -4 400 -2 5 0 300 10 200

2 Manatee Detection Distance (m) 4 100 0 6 0 Boat Distance (m) 0 200 400 Detection Threshold (dB) Boat Distance (m)

Figure 8-19. Maximum manatee detection ranges at NL =100 dB and SLB =125 dB after FALE is applied.

CHAPTER 9 REAL TIME SIMULATION

The detection range of the system with noise reduction has been estimated in

Chapter 8. In order to further verify the efficiency of the noise reduction algorithms, bandpass filter, FIR-ALE, and FALE, a test to detect manatees in real time using real recordings is desired. However, it is difficult to perform a field test using real manatees and boats in a river because of the logistical challenges. The manatees are not controllable and the combination of testing with actual manatees and boats is impractical and dangerous. Therefore, a feasible way to evaluate the noise reduction algorithms in the laboratory is to implement the algorithms in dSPACE to detect the prerecorded manatee vocalizations corrupted by background noise. The prerecorded manatee vocalizations selected for testing are from the recordings made by O’Shea (1981-1984).

The real time simulations based on dSPACE are performed by combining the technique of background noise cancellation and detection methods proposed by Niezrecki et al. (2003). These simulations are performed in a laboratory setting using recording input directly into dSPACE. This chapter will discuss how the experiments are set up to test the detection system enhanced by noise reduction. The main goal of this dissertation is to improve the SNR of the manatee vocalizations by reducing background noise and verify the improvement of the detection ability of the system that uses noise reduction.

Therefore, only the detection ability of the system using the threshold method (Niezrecki et al, 2003) and FIR-ALE will be evaluated in terms of the number of rate of correct detections, false detections, and missed calls. The detection ability of the system using

133 134 threshold method and FALE will not be evaluated due to the stability margin of FLAE.

Therefore, the comprehensive evaluation of the detection ability of the system with noise reduction using correct detection, false detection, and missed calls will not be investigated in this dissertation. A comprehensive description of three detection methods can be found in the work by Niezrecki et al. and Meyer (2003).

Experimental Laboratory Setup

The experimental laboratory setup is shown in Figure 9-1. The laboratory experiments are performed using a Sandisk MP3 player as the analog input to a DS 1005

PPC controller board equipped with 480MHz CPU. The signal from the MP3 player is used to simulate the signal measured by a hydrophone. The MP3 player is used to broadcast the manatee vocalizations corrupted by background noise including boat noise, snapping shrimp noise, and natural noise. An audio speaker is used to broadcast the original manatee vocalizations to allow the experimenter to distinguish the false detections and missed calls.

Figure 9-1. Experimental laboratory setup.

Simulink Block Diagrams and Implementation

The noise reduction algorithms, FIR-ALE and FALE, and detection method are designed in Simulink and complied into C code that can be executed in dSPACE. The

135

Simulink block diagrams are shown in Figure 9-2. The channel 1 of the dSPACE input block, DS2001_B1, provides the input signal to the system from the MP3 player. The function of this block is to convert the analog signal into a digital signal. The other channels are connected to terminators. Then this signal is multiplied by a gain of 50 to compensate for the controller board dividing the input signal by a factor of 10 and to increase the signal strength. The output of the input gain block is filtered by a bandpass filter defined by Eq. (6.1).

RTI Data Input Gain FDATool Detection algorithm ADC #1 50 Input Output Input output Trigger ADC #2 c Switch ADC #3 Digital ALE Counter Filter Design Constant ADC #4

ADC #5

DS2001_B1

Figure 9-2. Simulink block diagrams of the real time simulations.

The output of the bandpass filter is connected to the noise reduction block and the switch is used to turn the noise reduction algorithm on or off. The signal after the bandpass filter and ALE is connected to the input of the switch controlled by the constant

C. The switch is used to determine which signal is plugged into the detection algorithm part in real time simulations. The initial value of the constant is set to zero, which means that the noise reduction block is not included into the detection system at the beginning.

If the ON/OFF button (shown in Figure 9-10) is turned to ON, the noise reduction block will be included into the system

The ALE subsystem block shown in Figure 9-3 is used to reduce the background noise of manatee vocalizations. The ALE block is masked. That means that some parameters can be set by a window. The block parameter of ALE algorithm is shown in

136

Figure 9-4. Only the order and initial value of the weights are needed to be set before compiling in Simulink. The other parameters, such as step size, feedback constant, can be adjusted during the real time simulation. The order of ALE is set to 20 and the initial value of the filter taps is set to zero.

Feedback constant (Beta)

Sum Zero-Order Buffer 1-beta Delay Hold LMS To 1 1 -300 Reference z Sample Input narrow band 1 Pr imar y Output

Figure 9-3. ALE algorithm subsystem block.

Figure 9-4. Block parameters of ALE.

The LMS block is shown in Figure 9-5. As stated earlier, the step size is set to 0.1.

The initial state of the feedback constant of FALE is set to zero. As stated earlier, FALE is equivalent FIR-ALE when the feedback constant is zero. These two values are adjustable in the real time simulation. Therefore, the ALE algorithm can be changed from FIR-ALE to FALE in real time if necessary. A threshold in this block can be used to prevent the system from diverging. The threshold in these simulations is set to 1. That

137 means the weights of the ALE will be reset when the narrowband output of ALE is larger than the threshold.

[20x1] 1 y[k] [20x1] 1 Reference [20x1] narrowband

1 ste p si ze Unit Delay z Relational [20x1] 0.1 [20x1] Operator [20x1] [20x1] [20x1] W[k-1] In [20x1] 2 -1 > Rst z 1 Primary Filter Taps Threshold

Figure 9-5. LMS algorithm subsystem block.

The output of the noise reduction block is used as the input of the detection system.

The threshold method proposed by Niezrecki et al. (2003) is used in the detection part, which is shown Figure 9-6. A threshold is used to determine the presence of a manatee vocalization. From the Figure 9-6, the threshold detection method is implemented by taking the Fast Fourier Transform (FFT) of the input signal and tracking when the maximum value of the FFT exceeds a specified threshold.

Detection Gain output 1 5 FFT |u| max > signal Manatee Rst 1 Input Output Trigger FFT Complex to MinMax 16 Zero-Order Relational Buffer Magnitude-Angle Time Delay Hold Operator N-Sample 25 Enable

Threshold

Figure 9-6. Detection block with threshold detection method.

The buffer size is another important factor that affects the performance of detection. The size should be carefully selected so that it not only has enough frequency resolution but also gives a good frequency spectrum of manatee vocalizations in short time and averages the frequency spectrum of background noise as much as possible. The

138 computation of FFT will be a burden if the size is selected too large. In this method, the buffer is set to 512.

The threshold is set to 25 for the system with noise reduction and 170 for the system without noise reduction. The threshold for the detection system with noise reduction algorithm can be set much smaller than that for the system without a noise reduction algorithm. The value of the threshold is dependent on the sound pressure level of the input and the SNR of the manatee vocalizations. The counter block shown in

Figure 9-2 is used to count the number of detected manatee vocalizations.

The time delay subsystem in Figure 9-6 is used to check that a true output from the comparison block lasts long enough to be a manatee vocalization. The detail of this subsystem is shown in Figure 9-7. This subsystem is necessary to reject the snapping shrimp noise that typically has a much shorter duration than a manatee vocalization.

-1 1 z signal Integer Delay 1 -2 z

Integer Delay 2 -3 z

Integer Delay 3 -4 z

Integer Delay 4 -5 z >= 1 Integer Delay 5 Manatee 5 Relational -6 z Operator Time Delay Integer Delay 6 -7 z

Integer Delay 7 -8 z

Integer Delay 8 -9 z

Integer Delay 9 -10 z Integer Delay 10

Figure 9-7. Time delay subsystem block.

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The counter subsystem shown in Figure 9-8 is used to track the results of the detection method. The counter block counts the number of true output and is used to provide the counts input to the user count subsystem. A reset function is included to allow the experimenter to reset all of count results to zero. The user counter subsystem is shown in Figure 9-9. The subsystem can track three detection results: correct detection, false detection, and missed. Two pushbuttons in dSPACE are used to track false detection (or any calls missed by human hearing). Therefore, only audible manatee vocalizations are counted.

1 Clk 0 Trigger Up CntCnt Counts Rst # of Manatee Calls Counter Counts Reset

Reset 0 User Count

Figure 9-8. Counter subsystem block.

1 0 Counts Correct 0 Clk Up CntCnt 0 False Count 2 Rst # of False Detections Reset Counter 1

0 Clk 0 M i sse d Co u n t Up CntCnt Rst # of Missed calls Counter 2

Figure 9-9. System counter and user counter subsystem block.

dSPACE Layout

The dSPACE layout for real time simulations is shown in Figure 9-10. The light labeled by manatee detected will be on only when a manatee vocalization is detected. In a real scenario, some mechanism needs to keep the light flashing until the manatee swims

140 away from the detection area. The display labeled “# of manatee calls detected” displays the number that the system detects. The number is the sum of the correct detection and false alarm. In order to make the real time simulations more user friendly, input gain, detection gain, rejection threshold, step size, safety threshold, time delay, and feedback constant of ALE are all adjustable in the real time simulations.

An instantaneous realization of the real time simulation for the absence of the manatee vocalizations is shown in Figure 9-10. The interface of the real time simulation in dSPACE when a manatee vocalization is present is shown in Figure 9-11. There are three figures in the dSPACE layout to show the original manatee vocalizations corrupted by background noise, manatee vocalizations after bandpass filter is applied, and manatee vocalizations after ALE is applied, which are shown in top left, top right, and below left of Figure 9-10, respectively.

Figure 9-10. User interface of real time simulation in dSPACE when only noise is present.

141

Figure 9-11. The interface of the real time simulation in dSPACE when a manatee vocalization is present.

Simulation Results

The original recordings by Tom O’Shea were made using a Navy H-56 hydrophone and an Uher 4400 two-track tape recorder, operating at 19 cm/s (20–25 kHz bandwidth).

Then the recordings were converted to a digital format in 48 kHz, 16 bit stereo on two compact disks (O’Shea, 1981-1984).

Fifteen sequences described as contact cries and duets between cow and calves are selected for testing. Some of these resulted in a nursing episode so probably include some pre-nursing cries. The fifteen recordings are from the disk # 1 made by O’Shea.

These 15 tacks contain 360 audible manatee vocalizations along with background noise including the sounds of snapping shrimp, boat engine noise, bird-like calls, repetitive mechanical noise, and moving water sounds. A detailed description of each track,

142 including length, description of background noise, number of manatee vocalizations, and signal to noise ratio, is presented in Table 9-1.

Table 9-1. Description of tracks used for testing Track Length Description of background noise # of calls # (minutes) 1 1:53 Snapping shrimp 16 2 1:15 Snapping shrimp, moving water sounds 21 3 1:45 Constant snapping shrimp 27 Snapping shrimp, moving water sounds, engine noise 4 1:29 10 at the end of track 5 1:09 Snapping shrimp, hydrophone movement 9 Snapping shrimp, moving water sounds, quiet 6 3:09 49 manatee calls Snapping shrimp, moving water sound, hydrophone 7 1:10 27 movement 8 0:30 Snapping shrimp, low recording volume 9 9 0:41 Loud moving water 9 Snapping shrimp, sprinkler, loud moving water, some 10 3:05 44 low-level calls, low-level engine noise 11 0:52 Snapping shrimp, moving water sound 22 12 3:30 Snapping shrimp, moving water sound, sprinkler 51 Moving water sound, hydrophone movement, 13 1:18 33 snapping shrimp 14 1:09 Snapping shrimp, moving ware sound 11 15 0:57 Snapping shrimp moving water sound 22

As stated earlier, only the system using the threshold method enhanced by FIR-

ALE is evaluated in simulations in this dissertation. The threshold value is one of the most important factors for detection. There exists a tradeoff between the number of missed calls and the number of false alarms. The threshold value is determined by the

SPL of the input signal and SNR of manatee vocalizations. The real time simulations show that the background noise during different periods needs different thresholds to effectively reject noise. Therefore, the threshold needs to be selected carefully.

A track by track breakdown of the detection results of the system without noise reduction is shown in Table 9-2 and Figure 9-12. A track by track breakdown of the

143 detection results of the system with noise reduction Table 9-3 and Figure 9-13. The overall performance comparison between FIR-ALE and bandpass filter is shown in

Figure 9-14 and Table 9-4. These results show that the system enhanced by FIR-ALE decreased the missed detection rate from 20% to 5.3%.

Table 9-2. Detection results of the system without noise reduction for each track Track # # of Calls Correct Detections Missed calls False Detections 1 16 14 2 0 2 21 13 8 0 3 27 19 8 0 4 10 9 1 0 5 9 6 3 0 6 49 42 7 1 7 27 19 8 0 8 9 6 3 0 9 9 7 2 1 10 44 31 13 3 11 22 20 2 0 12 51 48 3 1 13 33 30 3 0 14 11 9 2 0 15 22 15 7 1

60 Correct Miss False Alarm 50

20 # of Manatee calls # of

0 123456789101112131415 Track #

Figure 9-12. Detection results of the system without noise reduction for each track.

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Table 9-3. Detection results of the system with noise reduction for each track Track # of Calls Correct Detections Missed calls False Detections # 1 16 16 0 0 2 21 17 4 0 3 27 24 3 0 4 10 10 0 0 5 9 8 1 0 6 49 47 2 1 7 27 25 2 0 8 9 8 1 0 9 9 9 0 1 10 44 41 3 3 11 22 22 0 0 12 51 51 0 1 13 33 33 0 0 14 11 10 1 0 15 22 20 2 1

60 Correct Miss False Alarm 50

20 # of Manatee# of calls

0 123456789101112131415 Track #

Figure 9-13. Detection results of the system with noise reduction for each track.

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400 Correct Miss False Alarm 350 300 250 200 Counts 150 100 50 0

Correct 288 341 Miss 72 19 False Alarm 77 Without noise reduction With noise reduction

Figure 9-14. Overall performance comparison between FIR-ALE and bandpass filter.

Table 9-4. Results of the comparison between the system without and with noise reduction Number Number Percent Number Percent Percent Method of of false false correct correct missed misses alarms alarms

Without noise 288 72 7 80.0 20.0 1.9 reduction

With noise 341 19 7 94.7 5.3 1.9 reduction

CHAPTER 10 CONCLUSIONS AND FUTURE WORK

Conclusions

An efficient method to extend the range of a manatee detection system by using background noise cancellation is proposed in this dissertation. Three methods, bandpass filter, FIR-ALE, and FALE, are implemented to reduce the background noise of manatee vocalizations. A library consisting 100 manatee vocalizations, which is divided into 10 different categories according to the frequency characteristic, is established to test these three algorithms. The performance of FIR-ALE and FALE are compared with a bandpass filter as baseline in terms of SNR estimates. The idea of SNR lower bound and upper bound is proposed to evaluate the performance of FIR-ALE and FALE when the

SNR of original manatee vocalizations varies from -25 dB to 0 dB. A proper range of the delay for FIR-ALE and FALE is given based on the manatee vocalizations in the established library. A field test is also performed on land to verify the performance of the three algorithms.

The improvements of the detection range of the system enhanced by FIR-ALE over bandpass filter and FALE over bandpass filter have been estimated, respectively. The improved detection ranges of the system enhanced by FIR-ALE and FALE have also been estimated by using a mixed spreading model, respectively. The improvements obtained by FIR-ALE and FALE show that the improved SNR can extend the detection range of the system.

146 147

The further evaluation for FIR-ALE over a bandpass filter is implemented in real time using a dSPACE DSP. In particular, the number of correct detections, false detections, and missed calls is evaluated. The missed detection rate decreased from 20% to 5.3%. The real time simulations show that the detection ability of the system can be improved by reducing the background noise of manatee vocalizations.

Future Work

This research represents the first effort to extend the range of manatee detection by using advanced signal processing techniques in order to extract manatee vocalizations that are buried in background noise. The following research topics should be investigated based on the present results

The community should investigate a strategy to optimize the step size of ALE algorithm. The step size of ALE should be kept large during the period of manatee vocalizations and small during the rest periods. It can be expected that the performance of ALE can be further improved with an optimized step size.

It is necessary to investigate the lowest SNRBPF (lower bound) that the system can detect a vocalization by only using a bandpass filter. As long as it is determined, the lower bound and upper bound for the improvement for the detection range of FIR-ALE and FALE over bandpass filter also can be determined from Figure 8-7.

In Chapter 9, real time simulations in dSPACE to detect the manatee vocalizations from actual recordings made by O’Shea are performed. However, only the performance of the detection system enhanced by FIR-ALE and threshold method is evaluated by the correct detection, false detection, and missed calls. The performance of the detection system enhanced by ALE including FIR-ALE and FALE with the other two detection

148 methods, harmonic content method and autocorrelation method, also need to be evaluated.

In Chapter 9, the discrimination threshold is fixed in the real time simulation. In signal detection theory, a Receiver Operating Characteristic (ROC) (also receiver operating curve) is a graphical relationship between the sensitivity and specificity for a binary classifier system as its discrimination threshold is varied (Swets and Pickett,

1982). That will provide a more comprehensive evaluation for the performance of FIR-

ALE and FALE.

All simulations in this dissertation are performed in MATLABTM, Simulink, and dSPACE. The performance of FIR-ALE and FALE are verified from several aspects in this dissertation. Although real recordings are used in these simulations, no detection experiments are performed in manatee’s habitats. It is a challenge to evaluate the performance of FIR-ALE and FALE by detecting the manatee vocalizations in their natural habitats.

Although FIR-ALE and FALE algorithms work well in reducing the background noise of manatee vocalizations, there are two promising noise reduction methods that may provide better performance. One is a nonlinear adaptive filter; the other is blind signal separation. These warrant further investigation.

Only linear adaptive filters are used to reduce the background noise of manatee vocalizations. These methods are limited by the inevitable misadjustment caused by weight noise. The nonlinearity of an adaptive filter may provide smaller error than linear adaptive filter.

149

In addition to the inevitable misadjustment, the leakage of the signal into the reference input places an upper bound on the performance of the ALE. The blind signal separation problem can be viewed as a generalization of the ANC problem. Therefore, blind signal separation approach may overcome some of the limitations of ANC described in Chapter 4 and has a potential advantage over ANC systems in applications where leakage is a problem.

APPENDIX A OPTIMAL DELAY PARAMETER OF ALE

The literature on the optimal delay parameter of ALE has been briefly reviewed in

Chapter 6. Some simulations in this appendix will continue to show the optimal delay of

ALE. All of the following simulations are based on a FIR structure ALE shown in Figure

4-4. In the following simulations, the primary input is a combination of sinusoids and white noise. The reference input is a delayed version of the primary input by ∆ time samples. The narrowband output of the adaptive filter is skˆ(), which is an estimate of the sinusoids.

The optimal delay for the case of one or two sinusoids corrupted by white noise with high SNR or arbitrary SNR has been derived (Zeiler et al., 1978; Reddy et al., 1981;

Egardt et al., 1983; Gupa, 1985; Yoganandam et al., 1988). The optimal delay for the case of one or two sinusoids corrupted by low-pass filtered white noise with the

assumption of high SNR has also been derived. The low-pass filtered white noise, nt , is assumed to be zero-mean with a covariance function given by Reddy et al. and Egardt et al. (1981, 1983).

2|ts− | cov(nnts , ) = σ nα (A.15)

2 where σ n is the power of the noise, α represents the correlation coefficient of the noise, and ts, are the delay time. For stationary signals, an iterative method has been proposed to find the optimal delay when the frequency spectrum of the original signal is unknown

(Zeiler et al., 1978; Reddy et al., 1981; Gupa, 1985; Yoganandam et al., 1988).

150 151

However, the optimal delay for the case of three or more sinusoids corrupted by white noise or band limited noise has not been derived. Three cases with one, two, and three sinusoids corrupted by white noise are simulated in this appendix. Compared to other two cases, the case of three sinusoids corrupted white noise is more similar to manatee problem.

The appendix is organized as follow. The evaluation criterion for ALE is discussed first. Three cases including one, two, and three sinusoids corrupted by white noise are simulated, which are shown in the following three sections, respectively. The common characteristics for these three cases are discussed as well. A new evaluation criterion for maximizing the SNR of the narrowband output is proposed. Lastly, some conclusions are drawn on the optimal delay and its factors.

Evaluation Criterion

What criterion should be used to pick a suitable delay? Intuitively, what we want is an estimate of the spectrum with sharp peaks at the true sinusoid frequencies. However, the final goal is to find an optimal delay to maximize the SNR of the narrowband output.

In particular, for the manatee problem, the final goal is to maximize the SNR between the estimated manatee call and the background noise in the absence of manatee call. There are two performance evaluation criteria presented in the literature. One is given by

Zeidler et al. (1978)

L−1 −∆+jkω() Hae()ω = ∑ k (A.16) k =0

where aaa012, , , " , aL− 1 are the weights of the adaptive filter and L represents the order of the adaptive filter. The other is also given by Egardt et al. (1983)

152

1 G()ω = (A.17) |1− H (ω )| where H (ω ) is the same as in Eq. (A.16). A new performance evaluation criterion based on the SNR of the narrowband output skˆ() will be proposed in this appendix.

However, simulations have shown that the first criterion, Eq. (A.16), will cause a frequency bias (Egardt et al., 1983). A signal that consists of two sinusoids with normalized frequencies 0.05 and 0.1 and white noise is used to illustrate this. The SNR for each sinusoid is set to 0 dB, and 10000 samples are used in simulation. The order and delay of adaptive filter are set to 18 and 13, respectively. The frequency spectrums of normalized H ()ω and normalized G()ω are shown in Figure A-1 and Figure A-2, respectively. The frequency spectrum of normalized G()ω has two sharp peaks due to its poles and the frequency spectrum of normalized H ()ω has a frequency bias.

Therefore, it is convenient to compare the performance of ALE with different delay if normalized G()ω is chosen as the evaluation criterion.

-5

-10

-15

-20

-25

-30

Normalized (dB) magnitude -35

-40

-45 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency Figure A-1. Frequency spectrum of normalized H ()ω when delay =13 and order =18.

153

-5

-10

-15

Normalized (dB) magnitude -20

-25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency Figure A-2. Frequency spectrum of normalized G()ω when delay =13 and order =18.

One Sinusoid Corrupted by White Noise

A signal that consists of one sinusoid with normalized frequency 0.025 and white noise is used in the simulation. The SNR is set to 0 dB. The order of the adaptive filter is set to 9, which is large enough to extract this sinusoid. Note that a large order renders the difference small between the performances of the ALE with different delay. In order to show a significant difference between them, a proper order should be chosen. Note that the Wiener solution is used to estimate the optimal weights of the adaptive filter because the signal is stationary.

The optimal delay for one sinusoid corrupted by white noise is given by Reddy et al. (1981)

ω0 (Lkk+ 2∆−=opt 1)π , integer (A.18)

where L represents the order of the adaptive filter and ω0 represents the normalized

radian frequency of the sinusoid. Even k should be chosen when ω0 L < π , and odd k

should be chosen when π ≤≤ωπ0 L 2 . In this case, the order L = 9 and

ω0 =×2ππ 0.025 = / 20 . Therefore,

154

9 ω L =××=0.025 2ππ 9 (A.19) 0 20

Therefore, even k should be chosen. From Eq. (3.4), we can obtain

kLπ (1)− ∆=opt − , k integer (A.20) 22ω0

The optimal delay should be

kπ (9− 1) ∆= − =10kk − 4, even integer (A.21) opt 2/202×π

Obviously, the optimal delay for this case is 16 when k=2 and is 36 when k=4, and so on.

The frequency spectrums of normalized G()ω with delay of 1 and 16 are shown in

Figure A-3. The performance of the large optimal value will be discussed later. The simulation shows that, although the white noise is uncorrelated with ∆= 1, ∆=1 is not the optimal choice that provides the best frequency estimate. That is to say, the optimal value provides an unbiased frequency estimate with sharpest peak and smallest side lobe.

0 delay=1 delay=16 -5

-10

-15

-20 Normalized (dB) magnitude -25

-30 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency Figure A-3. Frequency spectrum of normalized G()ω when delay= 1 and 16 and order=9.

155

If the normalized frequency is increased to 0.05, the optimal delay will be 6 when k=2. The frequency spectrums of normalized G()ω with delay of 1 and 6 are shown in

Figure A-4.

0 delay=1 delay=6

-5

-10

-15

Normalized magnitude (dB) magnitude Normalized -20

-25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency

Figure A-4. Frequency spectrums of normalized G()ω with delay of 1 and 6 and order=9.

Two Sinusoids Corrupted by White Noise

Two sinusoids with normalized frequency 0.05 and 0.1 and white noise are now used in the simulations. The two sinusoids have equal power (same in the following simulations). The SNR is set to 0 dB. The order of the adaptive filter is set to 15, which is a proper order to estimate the two sinusoids and is convenient to compare the results obtained by previous researchers. The optimal delay under high SNR derived by Egardt et al. (1983) is given by

δωπ(2∆optimal +−=Lnn 1) integer (A.22)

where δωω=−21 ω ,ω1 =⋅=0.05 2ππ /10 and ω2 = 0.1⋅= 2ππ / 5 . The optimal delay for this case is 57n − . The optimal delay will be 3, 8, 13, 18, 23, and so on. The optimal delay for arbitrary SNR derived by Yoganandam et al. is given by (1988)

156

δωπ(2∆optimal +−=Ln 1) nL even for δω< π (A.23) nL odd for π <δω< 2 π

The optimal delay for this case is 57n − , where odd n should be chosen. The optimal delay will be 8, 18, 28, and so on. The frequency spectrums of normalized G()ω , when delay is set to 1 and 8, are shown in Figure A-5. The simulation show that, although the white noise is uncorrelated with ∆ =1, ∆ =1 is not the optimal choice that provides the best frequency estimate.

0 delay=1 delay=8 -5

-10

-15

-20 Normalized magnitude (dB) Normalized magnitude -25

-30 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency Figure A-5. Frequency spectrum of normalized G()ω when delay= 1 and 8 and order=15.

Three Sinusoids Corrupted by White Noise

Three sinusoids with normalized frequency 0.05, 0.1, and 0.15 and white noise are used in simulations. The SNR is set to 0 dB. The three sinusoids have equal power. The order of the adaptive filter is set to 15, which is large enough to extract these three sinusoids. The optimal delay for the case of three sinusoids in white noise has not been derived, but the first step is to verify its existence via the simulations. The frequency spectrums of normalized G()ω , when the delay is set to 1 and 10, are shown in Figure

157

A-6. The simulation suggests that there exists an optimal delay for extracting the three sinusoids from white noise.

0 delay=1 delay=10 -5

-10

-15

-20 Normalized magnitude (dB) magnitude Normalized -25

-30 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency Figure A-6. Frequency spectrum of normalized G()ω when delay = 1 and 10 and order =15.

Common Characteristics for These Three Cases

From the previous sections, the simulations show that there exists an optimal delay for one, two, and three sinusoids corrupted by white noise. There also exist some common characteristics for these three cases.

From the Eq. (A.18), (A.22), and (A.23), the interval between two optimal values becomes smaller when the frequency or the frequency spacing between two sinusoids is increased.

For the case of one sinusoid in white noise, if the normalized frequency of the sinusoid is set to 0.15, the SNR is equal to 0 dB, and the order is set to 9, the frequency spectrums of normalized G()ω with delay of 6 and 15 are shown in Figure A-7 and

Figure A-8, respectively. The simulation shows that the side lobes of the frequency spectrum of normalized G()ω become larger when the delay is increased. If the order

158 of adaptive filter is increased from 10 to 20, the frequency spectrum of normalized

G()ω with order of 20 and delay of 18 is shown in Figure A-9. These simulations show that the side lobe can be reduced by increasing the order of the adaptive filter, but this approach will increase the computational complexity. It is believed that these properties also exist for the cases of two, three or more sinusoids in white noise.

-5

-10

-15 magnitude (dB) magnitude

-20

-25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 normalized frequency Figure A-7. Frequency spectrum of G()ω when delay =6 and order =9.

-2

-4

-6

-8

-10

-12 magnitude (dB) magnitude -14

-16

-18

-20 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 normalized frequency Figure A-8. Frequency spectrum of normalized G()ω when delay =15 and order =9.

159

-5

-10

-15 magnitude (dB) magnitude

-20

-25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 normalized frequency Figure A-9. Frequency spectrum of normalized G()ω when delay =18 and order=20.

0 delay=8 delay=28 -5

-10

-15

-20 Normalized magnitude(dB) -25

-30 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Normalized frequency Figure A-10. Frequency spectrum of normalized G()ω with delay of 8 and 28.

For the case of two sinusoids corrupted by white noise, there exist many choices for optimal delay with different k . For the case of two sinusoids shown in Figure A-5, if the formula (9) for arbitrary SNR is chosen to calculate the optimal value, the optimal value will be 8, 18, 28, and so on (Yoganandam et al., 1988). The frequency spectrum of normalized G()ω , when the delay is set to 8 and 28, is shown in Figure A-10. This figure shows that the frequency spectrum of normalized G()ω with delay 28 cause large

160 peaks in other frequencies. Therefore, G()ω is not the best criterion to evaluate the performance of each optimal delay.

Proposed Performance Evaluation Criterion

For some applications, the final goal is to improve the SNR of the narrowband output of the adaptive filter. Therefore, a new performance evaluation criterion, which is based on the estimated SNR of the narrowband output, is proposed in this section.

Two sinusoids with normalized frequencies 0.05 and 0.1 and white noise are used in the following simulations. The order of the Wiener filter is set to 15. The performance of FIR-ALE with delay from 1 to 100, when the SNR changes from -10 dB to 10 dB, is shown in Figure A-11. The simulation shows that the performance of the optimal value is 4 dB better than the worst one. The optimal value does not depend on the SNR of the original signal.

2 SNR after FIR-ALEis appliedSNR (dB) after 1

0 10 20 30 40 50 60 70 80 90 100 Delay Figure A-11. SNR after FIR-ALE is applied for the delay from 1 to 100 when order =15

Figure A-11 shows that the optimal value for this case is 20n − 7 , where n is integer. Therefore, the following formula that controls the optimal delay is inferred by

161

nL−1 ∆= − n integer (A.24) opt δ f 2

where ∆opt represents the optimal delay, δ f represents the frequency spacing, and L is the order of the Wiener filter.

From the Eq. (A.24), the ∆opt will increase if the frequency spacing δ f is decreased. Two sinusoids with normalized frequencies 0.15 and 0.175 and white noise are used in the simulation. The performance of FIR ALE with different delay, when the

SNR before ALE is applied is 0 dB, is shown in Figure A-12. The Figure shows that the optimal value has period of 40, which conforms to the formula (10).

SNR after FIR-ALE is FIR-ALE applied SNR(dB) after 0

-2 10 20 30 40 50 60 70 80 90 100 Delay Figure A-12. SNR after ALE with different delay when SNR before ALE is 0 dB

For a specific order, if Pmax and Pmin represents the maximum and minimum value of the SNR of the narrowband output for all delays, respectively, then ∆p is defined by

∆PP=−max P min (A.25)

The relationship between ∆P , L and δω is shown in Figure A-13, where L represents the order of adaptive filter and δω is the frequency difference between two sinusoids.

162

The simulations show that ∆P decreases as the order is increased and ∆P increases as

δω is decreased. The Figure shows that for delays that differ from the optimal, the performance difference, ∆P , becomes smaller as the order is increased.

18 ∆w=0.01 16 ∆w=0.02 ∆w=0.05 14 ∆w=0.1 ∆w=0.15 12

P (dB) 8 ∆

0 15 20 25 30 35 40 45 50 order L Figure A-13. The relationship between ∆PL, , and δω .

Conclusions

Three cases of one, two, and three sinusoids corrupted by white noise are simulated in this appendix. Simulations show that there exists an optimal delay for extracting the sinusoids from white noise. The optimal delay is a function of the order of adaptive filter and the frequency for the case of one sinusoid or the frequency spacing between the two for the case of two sinusoids and does not depend on the SNR. The optimal range of the delay will become wider as the order of adaptive filter is increased. The simulation also shows that there exists an optimal delay parameter for three sinusoids corrupted by white noise. The optimal delay for one or two sinusoids has been derived. However, the optimal delay for three sinusoids has not been derived due to its complexity.

APPENDIX B MANATEE VOCALIZATIONS IN THE LIBRARY

In order to clearly show the characteristics of manatee vocalizations in the library, ten manatee vocalizations of each category in time domain and their corresponding spectrograms are shown from Figure B-1 to Figure B-20. From these figures, it can be seen that some manatee vocalizations contain background noise.

All of the following spectrograms of the manatee vocalizations are obtained using

MATLABTM command “specgram”. A 256 point Kaiser window with beta of 2 is used in this command. The number of the overlap is set to 220.

163 164

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 Time (seconds)

Figure B-1. Manatee vocalizations from category 0000 in time domain.

100 20 80

60 15 40

10 0 Frequency (kHz) -20

5 -40

-60

0 0 1 2 3 4 5 Time (seconds)

Figure B-2. Spectrogram of manatee vocalizations from category 0000.

165

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-3. Manatee vocalizations from category 1000 in time domain.

100 20 80

60 15 40

10 0 Frequency (kHz) -20

5 -40

-60

0 0 1 2 3 4 5 6 Time (seconds)

Figure B-4. Spectrogram of manatee vocalizations from category 1000.

166

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 Time (seconds)

Figure B-5. Manatee vocalizations from category 1010 in time domain.

100

20 80

15 40

10 0 Frequency (kHz) -20

5 -40

-60

0 0 1 2 3 4 5 Time (seconds)

Figure B-6. Spectrogram of manatee vocalizations from category 1010.

167

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-7. Manatee vocalizations from category 1011 in time domain.

100 20 80

60 15 40

20 10 0 Frequency (kHz) -20

5 -40

-60

0 0 1 2 3 4 5 6 Time (seconds)

Figure B-8. Spectrogram of manatee vocalizations from category 1011.

168

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-9. Manatee vocalizations from category 1100 in time domain.

100

20 80

15 40

10 0 Frequency (kHz) -20

5 -40

-60

0 -80 0 1 2 3 4 5 6 Time (seconds)

Figure B-10. Spectrogram of manatee vocalizations from category 1100.

169

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-11. Manatee vocalizations from category 1110 in time domain.

100 20

15 60

10 20 Frequency (kHz)

0 5

-20

0 0 1 2 3 4 5 6 Time (seconds)

Figure B-12. Spectrogram of manatee vocalizations from category 1110

170

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-13. Manatee vocalizations from category 1111 in time domain.

100 20 80

15 40

10 0 Frequency (kHz) -20

5 -40

-60

0 0 1 2 3 4 5 6 Time (seconds)

Figure B-14. Spectrogram of manatee vocalizations from category 1111.

171

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-15. Manatee vocalizations from category 1200 in time domain.

120

100 20

15 60

10 20 Frequency (kHz)

0 5

-20

0 0 1 2 3 4 5 6 Time (seconds)

Figure B-16. Spectrogram of manatee vocalizations from category 1200.

172

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-17. Manatee vocalizations from category 1210 in time domain.

120

100 20 80

60 15 40

20 10 0 Frequency (kHz) -20 5 -40

-60

0 0 1 2 3 4 5 6 Time (seconds)

Figure B-18. Spectrogram of manatee vocalizations from category 1210.

173

0.4

0.3

0.2

0.1

0 Amplitude -0.1

-0.2

-0.3

-0.4 0 1 2 3 4 5 6 Time (seconds)

Figure B-19. Manatee vocalizations from category 1211 in time domain.

100

20 80

15 40

10 0 Frequency (kHz) -20

5 -40

-60

0 -80 0 1 2 3 4 5 6 Time (seconds)

Figure B-20. Spectrogram of manatee vocalizations from category 1211.

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BIOGRAPHICAL SKETCH

Zheng Yan was born in NanJing, China, 1977. He received his Bachelor of

Science degree and Master of Science degree in the Department of Mechanical

Engineering from NanJing University of Science and Technology in his hometown in

1999 and 2002.

Then he found his strong interest in adaptive signal processing and joined the

Department of Mechanical and Aerospace Engineering at the University of Florida for the PhD degree in 2002. Since then, he has continued his studies and worked as a research assistant with Dr. Christopher Niezrecki and Dr. Louis Cattafesta.

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