University of New Orleans ScholarWorks@UNO University of New Orleans Theses and Dissertations Dissertations and Theses 12-15-2006 Acoustic Seabed and Target Classification using rF actional Fourier Transform and Time-Frequency Transform Techniques Madalina Barbu University of New Orleans Follow this and additional works at: https://scholarworks.uno.edu/td Recommended Citation Barbu, Madalina, "Acoustic Seabed and Target Classification using rF actional Fourier Transform and Time-Frequency Transform Techniques" (2006). University of New Orleans Theses and Dissertations. 480. https://scholarworks.uno.edu/td/480 This Dissertation is protected by copyright and/or related rights. It has been brought to you by ScholarWorks@UNO with permission from the rights-holder(s). You are free to use this Dissertation in any way that is permitted by the copyright and related rights legislation that applies to your use. 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Acoustic Seabed and Target Classication using Fractional Fourier Transform and Time-Frequency Transform Techniques A Dissertation Submitted to the Graduate Faculty of the University of New Orleans in partial fulllment of the requirements for the degree of Doctor of Philosophy in Engineering and Applied Sciences by Madalina Barbu B.S./MS, Physics, University of Bucharest, Romania, 1993 MS, Electrical Engineering, University of New Orleans, 2001 December, 2006 c 2006, Madalina Barbu ii To my family iii Acknowledgments I would like to express my appreciation to Dr. Edit Bourgeois and Dr. Russell Trahan for supervising and reviewing the present dissertation. I would also like to thank Dr. Juliette Ioup, Dr. Dimitrios Charalampidis and Dr. Ralph Saxton for serving in the Ph D thesis defense committee. If it were not for the guidance of my committee, excellent education provided through my graduate studies, the patience and support of my family, this dissertation would not exist. I gratefully acknowledge Naval Research Laboratory for providing me data for testing my algorithm. Finally I acknowledge Reverend Cristian Prusan for his encouragement and prayers throughout the research process. iv Table of Contents List of Tables...................................................................................................................................................................................................vii List of Figures...................................................................................................................................................................................................x Abstract.............................................................................................................................................................................................................xiii Chapter 1 Introduction.......................................................................................................................................................................1 1.1 Sediment Classication..........................................................................................................................................................3 1.2 Target Classication ..............................................................................................................................................................10 1.3 Sonar Signal Processing.....................................................................................................................................................16 Chapter 2 System Description..................................................................................................................................................22 2.1 Volume Search Sonar (VSS)...........................................................................................................................................22 2.1.1 Receive Array. 23 2.1.2 Projector Array . 23 2.2 Parametric Sonar......................................................................................................................................................................24 2.2.1 Standard Parametric Sonar . 24 Chapter 3 Sonar Signal Enhancement using Fractional Fourier Transform ..........................................27 3.1 Introduction..................................................................................................................................................................................27 3.2 Fractional Fourier Transform Overview.................................................................................................................29 3.3 Application of the Fractional Fourier Transform ............................................................................................33 3.4 Experimental Results............................................................................................................................................................35 3.5 Conclusions..................................................................................................................................................................................41 3.6 Acknowledgements................................................................................................................................................................42 Chapter 4 Fractional Fourier Transform for Sonar Signal Processing.......................................................43 4.1 Introduction ................................................................................................................................................................................44 4.2 Theoretical Aspects................................................................................................................................................................46 4.2.1 Fractional Fourier Transform . 46 4.2.2 Wigner Distribution . 48 4.2.3 Singular Value Decomposition . 49 4.3 Application of the Fractional Fourier Transform for Sediment Classication..........................50 4.4 Conclusions..................................................................................................................................................................................57 4.5 Acknowledgments...................................................................................................................................................................58 Chapter 5 Acoustic Seabed Classication using Fractional Fourier Transform.................................59 5.1 Introduction ................................................................................................................................................................................59 5.2 Theoretical Aspects................................................................................................................................................................62 5.2.1 Fractional Fourier Transform . 62 5.2.2 Time-Frequency Analysis. 63 5.2.3 Singular Value Decomposition . 65 5.3 Approach........................................................................................................................................................................................66 v 5.4 Experimental Results............................................................................................................................................................68 5.5 Conclusions..................................................................................................................................................................................75 Chapter 6 Acoustic Seabed Classication using Fractional Fourier Transform and Time-Frequency Transform Techniques ..................................................................................................77 6.1 Introduction..................................................................................................................................................................................78 6.2 Theoretical Aspects................................................................................................................................................................80 6.2.1 Fractional Fourier Transform . 80 6.2.2 Time-Frequency Analysis. 81 6.2.3 Singular Value Decomposition . 83 6.3 Technique for Sediment Classication....................................................................................................................84 6.4 Experimental Results............................................................................................................................................................85 6.5 Conclusions..................................................................................................................................................................................89 Chapter 7 Experimental Results for Sediment Classication using Techniques on Sonar Data.......................................................................................................................................................................91 7.1 Introduction..................................................................................................................................................................................91