Fundamentals of Differential Beamforming (eBook)

Jacob Benesty received a Master’s degree in microwaves from Pierre & Marie Curie University, France, in 1987, and a Ph.D. degree in control and signal processing from Orsay University, France, in April 1991. During his Ph.D. (from Nov. 1989 to Apr. 1991), he worked on adaptive filters and fast algorithms at the Centre National d’Etudes des Telecommunications (CNET), Paris, France. From January 1994 to July 1995, he worked at Telecom Paris University on multichannel adaptive filters and acoustic echo cancellation. From October 1995 to May 2003, he was first a Consultant and then a Member of the Technical Staff at Bell Laboratories, Murray Hill, NJ, USA. In May 2003, he joined the University of Quebec, INRS-EMT, in Montreal, Quebec, Canada, as a Professor. He is also a Visiting Professor at the Technion, Haifa, in Israel, an Adjunct Professor at Aalborg University, in Denmark, and a Guest Professor at Northwestern Polytechnical University, Xi’an, Shaanxi, in China.   Jingdong Chen received the Ph.D. degree in pattern recognition and intelligence control from the Chinese Academy of Sciences in 1998. From 1998 to 1999, he was with ATR Interpreting Telecommunications Research Laboratories, Kyoto, Japan, where he conducted research on speech synthesis, speech analysis, as well as objective measurements for evaluating speech synthesis. He then joined the Griffith University, Brisbane, Australia, where he engaged in research on robust speech recognition and signal processing. From 2000 to 2001, he worked at ATR Spoken Language Translation Research Laboratories on robust speech recognition and speech enhancement. From 2001 to 2009, he was a Member of Technical Staff at Bell Laboratories, Murray Hill, New Jersey, working on acoustic signal processing for telecommunications. He subsequently joined WeVoice Inc. in New Jersey, serving as the Chief Scientist. He is currently a professor at the Northwestern Polytechnical University in Xi’an, China. His research interests include acoustic signal processing, adaptive signal processing, speech enhancement, adaptive noise/echo control, microphone array signal processing, signal separation, and speech communication.   Chao Pan received the Bachelor degree in electronics and information engineering from the Northwestern Polytechnical University (NPU) in 2011. He is currently a Ph.D. student in information and communication engineering at NPU and also a visiting Ph.D. student at INRS-EMT, University of Quebec. His research interests are in speech enhancement, noise reduction, and microphone array signal processing for hands-free speech communications.

Contents 6
Abstract 8
1 Introduction 10
1.1 Introduction 10
1.2 Microphone Array Beamforming: A Brief Overview 12
1.3 Differential Microphone Arrays 15
1.4 Differential Beamforming in the STFT Domain 17
1.5 Organization of the Book 19
References 20
2 Problem Formulation 22
2.1 Signal Model 22
2.2 Beampatterns 24
2.3 Front-to-Back Ratios 25
2.4 Signal-to-Noise Ratio Gains 27
2.5 Examples of Theoretical Differential Beamformers 30
References 35
3 Some Background 36
3.1 Linear Spaces 36
3.2 Orthogonal Functions 38
3.3 Orthogonal Polynomials 41
3.3.1 Legendre 44
3.3.2 Chebyshev 45
3.3.3 Jacobi 46
References 48
4 Performance Measures Revisited 49
4.1 Beampatterns 49
4.2 Weighted Front-to-Back Ratios 53
4.3 Weighted Directivity Factors 54
References 58
5 Conventional Optimization 59
5.1 Delay-and-Sum Beamformer 59
5.2 w-Hypercardioid 62
5.3 w-Supercardioid 69
5.4 Dipole and Cardioid 78
5.5 Tunable Differential Beamformer 82
References 86
6 Beampattern Design 88
6.1 Nonrobust Approach 88
6.2 Robust Approach 94
6.3 Constant Beampattern Design 99
6.4 Weighted Least-Squares Method 107
References 117
7 Joint Optimization 118
7.1 Preliminaries 118
7.2 Joint Optimization 120
References 127
Index 128