Companding Techniques for High Dynamic Range Audio CODEC Receiver Path by Yunjie Ma S.B. EE, MIT (2008) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2009 c Massachusetts Institute of Technology 2009. All rights reserved. Author............................................... ............... Department of Electrical Engineering and Computer Science May 22, 2009 Certified by........................................... ............... Guoqing Miao Director of Engineering, Qualcomm VI-A Company Thesis Supervisor Certified by........................................... ............... Vladimir Stojanovic Assistant Professor of Electrical Engineering M.I.T. Thesis Supervisor Accepted by........................................... .............. Arthur C. Smith Chairman, Department Committee on Graduate Theses 2 Companding Techniques for High Dynamic Range Audio CODEC Receiver Path by Yunjie Ma Submitted to the Department of Electrical Engineering and Computer Science on May 22, 2009, in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science Abstract In this thesis, an audio CODEC receiver path has been modified by the addition of companding techniques. Companding compresses the input signal and expands the output signal according to the input power strength such that additional noise from the system is suppressed while the signal content is maintained. As the compres- sion level is varied according to the input signal strength, transients occur at the output of the system. Sudden changes in the compression level cannot be processed instantaneously and generate transients in the output. The thesis first statically demonstrates that companding can increase the signal to noise ratio and improve the dynamic range of the audio CODEC Rx path by up to 18 dB. Further, two compen- sation techniques are analyzed in attempt to reduce the companding transients. The results show that transients in the output are reduced on average by 60% when using either compensation technique. VI-A Company Thesis Supervisor: Guoqing Miao Title: Director of Engineering, Qualcomm M.I.T. Thesis Supervisor: Vladimir Stojanovic Title: Assistant Professor of Electrical Engineering 3 4 Acknowledgments I am grateful to MIT, the Course VI department, and the VI-A program for providing me the opportunity to perform my Master of Engineering thesis at Qualcomm. I would like to thank Guoqing Miao, Song Wang, and Derick Hugunin at Qual- comm for their insight, support, and advice on my thesis. Our meetings always gave me ideas even when there seemed to be no other method. Thank you Professor Vladimir Stojanovic for your guidance throughout my thesis project. To my family and friends, thank you for always being there for me. And to Lawrence, with love. 5 6 Contents 1 Introduction 13 2 Marimba audio CODEC receiver path 17 2.1 DescriptionoftheRxpath. 18 2.2 Rxpathnoisesources........................... 19 2.3 Rxpathimprovements .......................... 20 3 Companding basics 21 3.1 Historyandapplications . 21 3.2 Thebenefitsofcompanding . 22 3.3 Instantaneouscompanding . 25 3.4 Syllabiccompanding ........................... 26 4 Apply companding to the audio CODEC Rx path 29 5 Syllabic companding and transients 33 5.1 Asimpleexample............................. 33 5.2 Frequencydomainanalysis. 35 5.3 Transientcompensationmethods . 35 5.3.1 Filter gain signal compensation . 37 5.3.2 Zero-crossings compensation . 38 6 Non-linear simulations: static companding 43 6.1 Simulationsetup ............................. 43 7 6.2 Simulationresults............................. 44 7 Non-linear simulations: dynamic companding 49 7.1 Simulationsetup ............................. 49 7.2 Exampleoutput.............................. 51 7.3 Simulationresults............................. 55 8 Conclusion 63 8.1 Recommendations............................. 63 A Other compensation methods 65 A.1 Systemcoefficientcorrection . 65 A.2 Feed-forwardaddcompensation . 66 8 List of Figures 2-1 BlockdiagramofaudioCODECRxpath. 17 2-2 ∆Σquantizationnoise .......................... 20 3-1 A typical analog signal processor . 23 3-2 TypicalinputtoSNDRrelationships . 24 3-3 Compressionandexpansion . 24 3-4 µ-law.................................... 25 3-5 Syllabiccompanding ........................... 26 3-6 Syllabiccompandingsignals . 27 4-1 Rxpathwithsyllabiccompanding. 30 4-2 Alternative Rx path with syllabic companding . 31 5-1 Rx path with syllabic companding and filter gain compensation . 37 5-2 Alternative Rx path with syllabic companding and filter gain compen- sation ................................... 38 5-3 Zero-crossing compensation - delay in gain level . 39 5-4 Rx path with syllabic companding and zero-crossing compensation . 40 6-1 Static companding at Fs =8KHzandOSR=256x. 45 6-2 Static companding at A = -60 dBFS and -100 dBFS DCT noise . 46 6-3 Static companding at A = -60 dBFS and -90 dBFS DCT noise . 47 7-1 Example of the companding gain level transitions . 52 7-2 Transient calculations with attenuation error . ...... 53 9 7-3 Exampleoutputsofthefoursystemssimulated . 53 7-4 Relative transient peaks as (g1, g2)varies................ 56 7-5 Zerocrossinganalysis........................... 58 7-6 Relative transient peaks as Fs andOSRvary.............. 59 7-7 Relative transient peaks with and without ±0.5 dB attenuation error 60 8-1 Companding - Compression Input-Output Curve . 64 A-1 Feedforward Compensation Block Diagram . 68 A-2 Rx path with syllabic companding and feedforward add compensation 69 10 List of Tables 6.1 Simulation Parameters for Static Companding . 44 6.2 Companding Dynamic Range Improvements . 48 7.1 Simulation Parameters for Dynamic Companding . 50 7.2 Average Transient Peak Amplitudes . 61 7.3 Average Transient Peak Amplitudes - % Decrease . 62 11 12 Chapter 1 Introduction This thesis aims to improve the audio CODEC receiver path of the Marimba chip, part of the Snapdragon chipset with features for Bluetooth, audio codec + touch screen, and FM transceiver/receiver. The thesis analyzes different companding systems to improve the dynamic range of the CODEC receiver path. Companding compresses the input signal and expands the output signal to keep the signal level above the noise level during processing. The static effects, improvements in SNR, and dynamic effects, transients caused by input power changes, of these companding techniques are analyzed in this paper. The thesis is divided into the following chapters. Chapter 2 describes existing Marimba CODEC receiver path, a system that con- verts a digital audio input into an analog signal to be played on the speaker or headset of a cellular phone. The goal of this thesis is to improve the signal to noise ratio (SNR) of the system for small input signals. Conventional analog techniques would consume too much power and therefore cannot be used to improve the SNR. Instead, the thesis will focus on different companding techniques. Chapter 3 describes the method of companding, a signal processing technique used to increase the dynamic range of systems. The formation of the word companding comes from the words compressing and expanding. Companding compresses the dynamic range of input signal and expands the dynamic range of the output signal so that the noise is suppressed while the signal is maintained. Since first patented by 13 A.B. Clark in 1928, companding has had a variety of applications in communication systems, audio recordings, and signal processing, see [1], [8], and [14]. Chapter 3 explains in detail the two type of companding systems that exist: instantaneous companding and syllabic companding. Chapter 4 describes how the thesis applies syllabic companding to the receiver path. Three additional system blocks are added to the receiver path: a root mean squared (RMS) power detector, a variable gain amplifier, and a variable gain attenu- ator. The amplifier acts as the compressor and the attenuator acts as the expander. The placement of the compressor and the expander minimizes the effects of the delta sigma quantization noise and the DCT (direct charge transfer) analog noise. Chapter 5 describes the transients that are inadvertently caused by the new com- panding system. These transients are formed when a change in the input signal power level is detected. The change is not processed instantaneously by the companding sys- tem, causing transients to form. Different methods to reduce the transients are dis- cussed in this chapter. These compensation techniques include adding an additional delay in the expander control path and manipulating the control path to change the signals at more optimal times. Chapter 6 describes the first set of simulations: static simulations. The transients are first ignored to study SNR improvements in the audio CODEC receiver path with companding. By keeping the compressor and expander gain levels constant, the transients disappear. The simulations test the companding system with various input amplitudes, compression levels, sampling frequencies, and over-sampling ratios (OSR). Chapter 7 describes the dynamic simulations of the audio CODEC receiver path with companding. In addition to the original companding system, these simulations test the two compensation methods discussed in Chapter 5. The transients are pro- duced in the output by changing