Subband adaptive filtering theory and implementation

Subband adaptive filtering is rapidly becoming one of the most effective techniques for reducing computational complexity and improving the convergence rate of algorithms in adaptive signal processing applications. This book provides an introductory, yet extensive guide on the theory of various subband adaptive filtering techniques. For beginners, the authors discuss the basic principles that underlie the design and implementation of subband adaptive filters. For advanced readers, a comprehensive coverage of recent developments, such as multiband tap-weight adaptation, delayless architectures, and filter-bank design methods for reducing band-edge effects are included. Several analysis techniques and complexity evaluation are also introduced in this book to provide better understanding of subband adaptive filtering. This book bridges the gaps between the mixed-domain natures of subband adaptive filtering techniques and provides enough depth to the material augmented by many MATLAB® functions and examples.

Key Features:

Acts as a timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications. Bridges the gaps between two distinct domains: adaptive filter theory and multirate signal processing. Uses a practical approach through MATLAB®-based source programs on the accompanying CD. Includes more than 100 M-files, allowing readers to modify the code for different algorithms and applications and to gain more insight into the theory and concepts of subband adaptive filters.

Subband Adaptive Filtering is aimed primarily at practicing engineers, as well as senior undergraduate and graduate students. It will also be of interest to researchers, technical managers, and computer scientists.

Author Notes

Kong-Aik Lee received his B.Eng (1st Class Hons) degree from Universiti Teknologi Malaysia in 1999, and his Ph.D. degree from Nanyang Technological University, Singapore, in 2006. He is currently a Research Fellow with the Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A∗STAR), Singapore. He has been actively involved in the research on subband adaptive filtering techniques for the past few years. He invented the Multiband-structured Subband Adaptive Filter (MSAF), a very fast converging and computationally efficient subband adaptive filtering algorithm. His current research has primarily focused on improved classifier design for speaker and language recognition.

Woon-Seng Gan received his B.Eng (1st Class Hons) and PhD degrees, both in Electrical and Electronic Engineering from the University of Strathclyde, UK in 1989 and 1993 respectively. He joined the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, as a Lecturer and Senior Lecturer in 1993 and 1998 respectively. In 1999, he was promoted to Associate Professor. He is currently the Deputy Director of the Center for Signal Processing at Nanyang Technological University. His research interests include adaptive signal processing, psycho-acoustical signal processing, audio processing, and real-time embedded systems. He has published more than 170 international refereed journals and conference papers, and has been awarded four Singapore and US patents. He has previously co-authored two technical books on Digital Signal Processors: Architectures, Implementations, and Applications (Prentice Hall, 2005) and Embedded Signal Processing with the Micro Signal Architecture (Wiley-IEEE, 2007).
Dr. Gan has also won the Institute of Engineers Singapore (IES) Prestigious Engineering Achievement Award in 2001 for his work on Audio Beam System. He is currently serving as an Associate Editor for the EURASIP Journal on Audio, Speech and Music Processing, and EURASIP Research Letters in Signal Processing. He is also a Senior Member of IEEE and serves as a committee member in the IEEE Signal Processing Society Education Technical Committee.

Sen M. Kuo received the B.S. degree from National Taiwan Normal University, Taipei, Taiwan, in 1976 and the M.S. and Ph.D. degrees from the University of New Mexico, Albuquerque, NM in 1983 and 1985, respectively. He is a Professor and served as the department chair from 2002 to 2008 in the Department of Electrical Engineering, Northern Illinois University, DeKalb, IL. He was with Texas Instruments, Houston, TX in 1993, and with Chung-Ang University, Seoul, Korea in 2008. He is the leading author of four books: Active Noise Control Systems (Wiley, 1996), Real-Time Digital Signal Processing (Wiley, 2001, 2006), and Digital Signal Processors (Prentice Hall, 2005), and a co-author of Embedded Signal Processing with the Micro Signal Architecture (Wiley 2007). He holds seven US patents, and has published over 200 technical papers. His research focuses on active noise and vibration control, real-time DSP applications, adaptive echo and noise cancellation, digital audio and communication applications, and biomedical signal processing. Prof. Kuo received the IEEE first-place transactions (Consumer Electronics) paper award in 1993, and the faculty-of-year award in 2001 for accomplishments in research and scholarly areas. He served as an associate editor for IEEE Transactions on Audio, Speech and Language Processing, and serves as a member of the editorial boards for EURASIP Research Letters in Signal Processing and Journal of Electrical and Computer Engineering.

About the authors	p. xi
Preface	p. xiii
Acknowledgments	p. xv
List of symbols	p. xvii
List of abbreviations	p. xix
1 Introduction to adaptive filters	p. 1
1.1 Adaptive filtering	p. 1
1.2 Adaptive transversal filters	p. 2
1.3 Performance surfaces	p. 4
1.4 Adaptive algorithms	p. 6
1.5 Spectral dynamic range and misadjustment	p. 13
1.6 Applications of adaptive filters	p. 15
1.6.1 Adaptive system identification	p. 15
1.6.2 Adaptive prediction	p. 23
1.6.3 Adaptive inverse modeling	p. 25
1.6.4 Adaptive array processing	p. 28
1.6.5 Summary of adaptive filtering applications	p. 31
1.7 Transform-domain and subband adaptive filters	p. 31
1.7.1 Transform-domain adaptive filters	p. 31
1.7.2 Subband adaptive filters	p. 38
1.8 Summary	p. 39
References	p. 39
2 Subband decomposition and multirate systems	p. 41
2.1 Multirate systems	p. 41
2.2 Filter banks	p. 44
2.2.1 Input-output relation	p. 46
2.2.2 Perfect reconstruction filter banks	p. 47
2.2.3 Polyphase representation	p. 48
2.3 Paraunitary filter banks	p. 54
2.4 Block transforms	p. 55
2.4.1 Filter bank as a block transform	p. 55
2.5 Cosine-modulated filter banks	p. 59
2.5.1 Design example	p. 63
2.6 DFT filter banks	p. 65
2.6.1 Design example	p. 66
2.7 A note on cosine modulation	p. 67
2.8 Summary	p. 68
References	p. 69
3 Second-order characterization of multirate filter banks	p. 73
3.1 Correlation-domain formulation	p. 73
3.1.1 Critical decimation	p. 77
3.2 Cross spectrum	p. 79
3.2.1 Subband spectrum	p. 82
3.3 Orthogonality at zero lag	p. 85
3.3.1 Paraunitary condition	p. 86
3.4 Case study: Subband orthogonality of cosine-modulated filter banks	p. 89
3.4.1 Correlation-domain analysis	p. 89
3.4.2 MATLAB simulations	p. 92
3.5 Summary	p. 96
References	p. 97
4 Subband adaptive filters	p. 99
4.1 Subband adaptive filtering	p. 99
4.1.1 Computational reduction	p. 100
4.1.2 Spectral dynamic range	p. 101
4.2 Subband adaptive filter structures	p. 104
4.2.1 Open-loop structures	p. 104
4.2.2 Closed-loop structures	p. 104
4.3 Aliasing, band-edge effects and solutions	p. 106
4.3.1 Aliasing and band-edge effects	p. 107
4.3.2 Adaptive cross filters	p. 108
4.3.3 Multiband-structured SAF	p. 110
4.3.4 Closed-loop delayless structures	p. 113
4.4 Delayless subband adaptive filters	p. 114
4.4.1 Closed-loop configuration	p. 114
4.4.2 Open-loop configuration	p. 115
4.4.3 Weight transformation	p. 116
4.4.4 Computational requirements	p. 123
4.5 MATLAB examples	p. 124
4.5.1 Aliasing and band-edge effects	p. 125
4.5.2 Delayless alias-free SAFs	p. 126
4.6 Summary	p. 128
References	p. 129
5 Critically sampled and oversampled subband structures	p. 133
5.1 Variants of critically sampled subband adaptive filters	p. 133
5.1.1 SAF with the affine projection algorithm	p. 134
5.1.2 SAF with variable step sizes	p. 136
5.1.3 SAF with selective coefficient update	p. 137
5.2 Oversampled and nonuniform subband adaptive filters	p. 138
5.2.1 Oversampled subband adaptive filtering	p. 138
5.2.2 Nonuniform subband adaptive filtering	p. 140
5.3 Filter bank design	p. 141
5.3.1 Generalized DFT filter banks	p. 141
5.3.2 Single-sideband modulation filter banks	p. 142
5.3.3 Filter design criteria for DFT filter banks	p. 144
5.3.4 Quadrature mirror filter banks	p. 149
5.3.5 Pseudo-quadrature mirror filter banks	p. 153
5.3.6 Conjugate quadrature filter banks	p. 155
5.4 Case study: Proportionate subband adaptive filtering	p. 156
5.4.1 Multiband structure with proportionate adaptation	p. 156
5.4.2 MATLAB simulations	p. 157
5.5 Summary	p. 161
References	p. 163
6 Multiband-structured subband adaptive filters	p. 167
6.1 Multiband structure	p. 167
6.1.1 Polyphase implementation	p. 170
6.2 Multiband adaptation	p. 173
6.2.1 Principle of minimal disturbance	p. 173
6.2.2 Constrained subband updates	p. 173
6.2.3 Computational complexity	p. 175
6.3 Underdetermined least-squares solutions	p. 177
6.3.1 NLMS equivalent	p. 178
6.3.2 Projection interpretation	p. 179
6.4 Stochastic interpretations	p. 179
6.4.1 Stochastic approximation to Newton's method	p. 179
6.4.2 Weighted MSE criterion	p. 181
6.4.3 Decorrelating properties	p. 186
6.5 Filter bank design issues	p. 187
6.5.1 The diagonal assumption	p. 187
6.5.2 Power complementary filter bank	p. 187
6.5.3 The number of subbands	p. 188
6.6 Delayless MSAF	p. 189
6.6.1 Open-loop configuration	p. 189
6.6.2 Closed-loop configuration	p. 191
6.7 MATLAB examples	p. 192
6.7.1 Convergence of the MSAF algorithm	p. 193
6.7.2 Subband and time-domain constraints	p. 195
6.8 Summary	p. 198
References	p. 199
7 Stability and performance analysis	p. 203
7.1 Algorithm, data model and assumptions	p. 203
7.1.1 The MSAF algorithm	p. 203
7.1.2 Linear data model	p. 204
7.1.3 Paraunitary filter banks	p. 206
7.2 Multiband MSE function	p. 209
7.2.1 MSE functions	p. 209
7.2.2 Excess MSE	p. 210
7.3 Mean analysis	p. 211
7.3.1 Projection interpretation	p. 211
7.3.2 Mean behavior	p. 213
7.4 Mean-square analysis	p. 214
7.4.1 Energy conservation relation	p. 214
7.4.2 Variance relation	p. 216
7.4.3 Stability of the MSAF algorithm	p. 216
7.4.4 Steady-state excess MSE	p. 217
7.5 MATLAB examples	p. 219
7.5.1 Mean of the projection matrix	p. 219
7.5.2 Stability bounds	p. 220
7.5.3 Steady-state excess MSE	p. 222
7.6 Summary	p. 223
References	p. 224
8 New research directions	p. 227
8.1 Recent research on filter bank design	p. 227
8.2 New SAF structures and algorithms	p. 228
8.2.1 In-band aliasing cancellation	p. 228
8.2.2 Adaptive algorithms for the SAF	p. 230
8.2.3 Variable tap lengths for the SAF	p. 230
8.3 Theoretical analysis	p. 232
8.4 Applications of the SAF	p. 232
8.5 Further research on a multiband-structured SAF	p. 233
8.6 Concluding remarks	p. 234
References	p. 235
Appendix A Programming in MATLAB	p. 241
A.l MATLAB fundamentals	p. 241
A.l.l Starting MATLAB	p. 241
A.1.2 Constructing and manipulating matrices	p. 244
A.1.3 The colon operator	p. 244
A.1.4 Data types	p. 248
A.1.5 Working with strings	p. 248
A.1.6 Cell arrays and structures	p. 249
A.1.7 MATLAB scripting with M-files	p. 251
A.1.8 Plotting in MATLAB	p. 252
A.1.9 Other useful commands and tips	p. 255
A.2 Signal processing toolbox	p. 258
A.2.1 Quick fact about the signal processing toolbox	p. 258
A.2.2 Signal processing tool	p. 262
A.2.3 Window design and analysis tool	p. 267
A.3 Filter design toolbox	p. 268
A.3.1 Quick fact about the filter design toolbox	p. 268
A.3.2 Filter design and analysis tool	p. 269
A.3.3 MATLAB functions for adaptive filtering	p. 270
A.3.4 A case study: adaptive noise cancellation	p. 272
Appendix B Using MATLAB for adaptive filtering and subband adaptive filtering	p. 279
B.1 Digital signal processing	p. 279
B.1.1 Discrete-time signals and systems	p. 279
B.1.2 Signal representations in MATLAB	p. 280
B.2 Filtering and adaptive filtering in MATLAB	p. 282
B.2.1 FIR filtering	p. 282
B.2.2 The LMS adaptive algorithm	p. 284
B.2.3 Anatomy of the LMS code in MATLAB	p. 285
B.3 Multirate and subband adaptive filtering	p. 292
B.3.1 Implementation of multirate filter banks	p. 292
B.3.2 Implementation of a subband adaptive filter	p. 297
Appendix C Summary of MATLAB scripts, functions, examples and demos	p. 301
Appendix D Complexity analysis of adaptive algorithms	p. 307
Index	p. 317

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