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简介
This book provides an introductory but extensive guide to the theories behind various subband adaptive filtering techniques. The authors also provide MATLAB-based examples, applications and exercises to demonstrate the basic principles underlying subband adaptive filter production for beginners and people unused to working with subband adaptive filters. The comprehensive coverage of recent developments such as multi-width tap-weight adaptation, delayless architectures and filterbank design for band-edge effects enables advanced readers to keep up-to-date with the industry. A timely introduction for researchers, graduate students and engineers who want to design and deploy subband adaptive filters in their research and applications. Focuses on the important and advanced area of subband adaptive filtering, with information on new research directions and experiments. Includes ready-to-run MATLAB-based source programmes on the included CD, allowing readers to modify the code for different algorithms and applications and gain more insight into the theory and concepts of subband adaptive filters. Contains chapters on subband decomposition, orthogonality of multirate filter banks, critically-sampled and oversampled subband systems, multiband systems and delayless subband adaptive filters.
目录
About the authors p. xi
Preface p. xiii
Acknowledgments p. xv
List of symbols p. xvii
List of abbreviations p. xix
Introduction to adaptive filters p. 1
Adaptive filtering p. 1
Adaptive transversal filters p. 2
Performance surfaces p. 4
Adaptive algorithms p. 6
Spectral dynamic range and misadjustment p. 13
Applications of adaptive filters p. 15
Adaptive system identification p. 15
Adaptive prediction p. 23
Adaptive inverse modeling p. 25
Adaptive array processing p. 28
Summary of adaptive filtering applications p. 31
Transform-domain and subband adaptive filters p. 31
Transform-domain adaptive filters p. 31
Subband adaptive filters p. 38
Summary p. 39
References p. 39
Subband decomposition and multirate systems p. 41
Multirate systems p. 41
Filter banks p. 44
Input-output relation p. 46
Perfect reconstruction filter banks p. 47
Polyphase representation p. 48
Paraunitary filter banks p. 54
Block transforms p. 55
Filter bank as a block transform p. 55
Cosine-modulated filter banks p. 59
Design example p. 63
DFT filter banks p. 65
Design example p. 66
A note on cosine modulation p. 67
Summary p. 68
References p. 69
Second-order characterization of multirate filter banks p. 73
Correlation-domain formulation p. 73
Critical decimation p. 77
Cross spectrum p. 79
Subband spectrum p. 82
Orthogonality at zero lag p. 85
Paraunitary condition p. 86
Case study: Subband orthogonality of cosine-modulated filter banks p. 89
Correlation-domain analysis p. 89
MATLAB simulations p. 92
Summary p. 96
References p. 97
Subband adaptive filters p. 99
Subband adaptive filtering p. 99
Computational reduction p. 100
Spectral dynamic range p. 101
Subband adaptive filter structures p. 104
Open-loop structures p. 104
Closed-loop structures p. 104
Aliasing, band-edge effects and solutions p. 106
Aliasing and band-edge effects p. 107
Adaptive cross filters p. 108
Multiband-structured SAF p. 110
Closed-loop delayless structures p. 113
Delayless subband adaptive filters p. 114
Closed-loop configuration p. 114
Open-loop configuration p. 115
Weight transformation p. 116
Computational requirements p. 123
MATLAB examples p. 124
Aliasing and band-edge effects p. 125
Delayless alias-free SAFs p. 126
Summary p. 128
References p. 129
Critically sampled and oversampled subband structures p. 133
Variants of critically sampled subband adaptive filters p. 133
SAF with the affine projection algorithm p. 134
SAF with variable step sizes p. 136
SAF with selective coefficient update p. 137
Oversampled and nonuniform subband adaptive filters p. 138
Oversampled subband adaptive filtering p. 138
Nonuniform subband adaptive filtering p. 140
Filter bank design p. 141
Generalized DFT filter banks p. 141
Single-sideband modulation filter banks p. 142
Filter design criteria for DFT filter banks p. 144
Quadrature mirror filter banks p. 149
Pseudo-quadrature mirror filter banks p. 153
Conjugate quadrature filter banks p. 155
Case study: Proportionate subband adaptive filtering p. 156
Multiband structure with proportionate adaptation p. 156
MATLAB simulations p. 157
Summary p. 161
References p. 163
Multiband-structured subband adaptive filters p. 167
Multiband structure p. 167
Polyphase implementation p. 170
Multiband adaptation p. 173
Principle of minimal disturbance p. 173
Constrained subband updates p. 173
Computational complexity p. 175
Underdetermined least-squares solutions p. 177
NLMS equivalent p. 178
Projection interpretation p. 179
Stochastic interpretations p. 179
Stochastic approximation to Newton's method p. 179
Weighted MSE criterion p. 181
Decorrelating properties p. 186
Filter bank design issues p. 187
The diagonal assumption p. 187
Power complementary filter bank p. 187
The number of subbands p. 188
Delayless MSAF p. 189
Open-loop configuration p. 189
Closed-loop configuration p. 191
MATLAB examples p. 192
Convergence of the MSAF algorithm p. 193
Subband and time-domain constraints p. 195
Summary p. 198
References p. 199
Stability and performance analysis p. 203
Algorithm, data model and assumptions p. 203
The MSAF algorithm p. 203
Linear data model p. 204
Paraunitary filter banks p. 206
Multiband MSE function p. 209
MSE functions p. 209
Excess MSE p. 210
Mean analysis p. 211
Projection interpretation p. 211
Mean behavior p. 213
Mean-square analysis p. 214
Energy conservation relation p. 214
Variance relation p. 216
Stability of the MSAF algorithm p. 216
Steady-state excess MSE p. 217
MATLAB examples p. 219
Mean of the projection matrix p. 219
Stability bounds p. 220
Steady-state excess MSE p. 222
Summary p. 223
References p. 224
New research directions p. 227
Recent research on filter bank design p. 227
New SAF structures and algorithms p. 228
In-band aliasing cancellation p. 228
Adaptive algorithms for the SAF p. 230
Variable tap lengths for the SAF p. 230
Theoretical analysis p. 232
Applications of the SAF p. 232
Further research on a multiband-structured SAF p. 233
Concluding remarks p. 234
References p. 235
Programming in MATLAB p. 241
MATLAB fundamentals p. 241
Starting MATLAB p. 241
Constructing and manipulating matrices p. 244
The colon operator p. 244
Data types p. 248
Working with strings p. 248
Cell arrays and structures p. 249
MATLAB scripting with M-files p. 251
Plotting in MATLAB p. 252
Other useful commands and tips p. 255
Signal processing toolbox p. 258
Quick fact about the signal processing toolbox p. 258
Signal processing tool p. 262
Window design and analysis tool p. 267
Filter design toolbox p. 268
Quick fact about the filter design toolbox p. 268
Filter design and analysis tool p. 269
MATLAB functions for adaptive filtering p. 270
A case study: adaptive noise cancellation p. 272
Using MATLAB for adaptive filtering and subband adaptive filtering p. 279
Digital signal processing p. 279
Discrete-time signals and systems p. 279
Signal representations in MATLAB p. 280
Filtering and adaptive filtering in MATLAB p. 282
FIR filtering p. 282
The LMS adaptive algorithm p. 284
Anatomy of the LMS code in MATLAB p. 285
Multirate and subband adaptive filtering p. 292
Implementation of multirate filter banks p. 292
Implementation of a subband adaptive filter p. 297
Summary of MATLAB scripts, functions, examples and demos p. 301
Complexity analysis of adaptive algorithms p. 307
Index p. 317
Preface p. xiii
Acknowledgments p. xv
List of symbols p. xvii
List of abbreviations p. xix
Introduction to adaptive filters p. 1
Adaptive filtering p. 1
Adaptive transversal filters p. 2
Performance surfaces p. 4
Adaptive algorithms p. 6
Spectral dynamic range and misadjustment p. 13
Applications of adaptive filters p. 15
Adaptive system identification p. 15
Adaptive prediction p. 23
Adaptive inverse modeling p. 25
Adaptive array processing p. 28
Summary of adaptive filtering applications p. 31
Transform-domain and subband adaptive filters p. 31
Transform-domain adaptive filters p. 31
Subband adaptive filters p. 38
Summary p. 39
References p. 39
Subband decomposition and multirate systems p. 41
Multirate systems p. 41
Filter banks p. 44
Input-output relation p. 46
Perfect reconstruction filter banks p. 47
Polyphase representation p. 48
Paraunitary filter banks p. 54
Block transforms p. 55
Filter bank as a block transform p. 55
Cosine-modulated filter banks p. 59
Design example p. 63
DFT filter banks p. 65
Design example p. 66
A note on cosine modulation p. 67
Summary p. 68
References p. 69
Second-order characterization of multirate filter banks p. 73
Correlation-domain formulation p. 73
Critical decimation p. 77
Cross spectrum p. 79
Subband spectrum p. 82
Orthogonality at zero lag p. 85
Paraunitary condition p. 86
Case study: Subband orthogonality of cosine-modulated filter banks p. 89
Correlation-domain analysis p. 89
MATLAB simulations p. 92
Summary p. 96
References p. 97
Subband adaptive filters p. 99
Subband adaptive filtering p. 99
Computational reduction p. 100
Spectral dynamic range p. 101
Subband adaptive filter structures p. 104
Open-loop structures p. 104
Closed-loop structures p. 104
Aliasing, band-edge effects and solutions p. 106
Aliasing and band-edge effects p. 107
Adaptive cross filters p. 108
Multiband-structured SAF p. 110
Closed-loop delayless structures p. 113
Delayless subband adaptive filters p. 114
Closed-loop configuration p. 114
Open-loop configuration p. 115
Weight transformation p. 116
Computational requirements p. 123
MATLAB examples p. 124
Aliasing and band-edge effects p. 125
Delayless alias-free SAFs p. 126
Summary p. 128
References p. 129
Critically sampled and oversampled subband structures p. 133
Variants of critically sampled subband adaptive filters p. 133
SAF with the affine projection algorithm p. 134
SAF with variable step sizes p. 136
SAF with selective coefficient update p. 137
Oversampled and nonuniform subband adaptive filters p. 138
Oversampled subband adaptive filtering p. 138
Nonuniform subband adaptive filtering p. 140
Filter bank design p. 141
Generalized DFT filter banks p. 141
Single-sideband modulation filter banks p. 142
Filter design criteria for DFT filter banks p. 144
Quadrature mirror filter banks p. 149
Pseudo-quadrature mirror filter banks p. 153
Conjugate quadrature filter banks p. 155
Case study: Proportionate subband adaptive filtering p. 156
Multiband structure with proportionate adaptation p. 156
MATLAB simulations p. 157
Summary p. 161
References p. 163
Multiband-structured subband adaptive filters p. 167
Multiband structure p. 167
Polyphase implementation p. 170
Multiband adaptation p. 173
Principle of minimal disturbance p. 173
Constrained subband updates p. 173
Computational complexity p. 175
Underdetermined least-squares solutions p. 177
NLMS equivalent p. 178
Projection interpretation p. 179
Stochastic interpretations p. 179
Stochastic approximation to Newton's method p. 179
Weighted MSE criterion p. 181
Decorrelating properties p. 186
Filter bank design issues p. 187
The diagonal assumption p. 187
Power complementary filter bank p. 187
The number of subbands p. 188
Delayless MSAF p. 189
Open-loop configuration p. 189
Closed-loop configuration p. 191
MATLAB examples p. 192
Convergence of the MSAF algorithm p. 193
Subband and time-domain constraints p. 195
Summary p. 198
References p. 199
Stability and performance analysis p. 203
Algorithm, data model and assumptions p. 203
The MSAF algorithm p. 203
Linear data model p. 204
Paraunitary filter banks p. 206
Multiband MSE function p. 209
MSE functions p. 209
Excess MSE p. 210
Mean analysis p. 211
Projection interpretation p. 211
Mean behavior p. 213
Mean-square analysis p. 214
Energy conservation relation p. 214
Variance relation p. 216
Stability of the MSAF algorithm p. 216
Steady-state excess MSE p. 217
MATLAB examples p. 219
Mean of the projection matrix p. 219
Stability bounds p. 220
Steady-state excess MSE p. 222
Summary p. 223
References p. 224
New research directions p. 227
Recent research on filter bank design p. 227
New SAF structures and algorithms p. 228
In-band aliasing cancellation p. 228
Adaptive algorithms for the SAF p. 230
Variable tap lengths for the SAF p. 230
Theoretical analysis p. 232
Applications of the SAF p. 232
Further research on a multiband-structured SAF p. 233
Concluding remarks p. 234
References p. 235
Programming in MATLAB p. 241
MATLAB fundamentals p. 241
Starting MATLAB p. 241
Constructing and manipulating matrices p. 244
The colon operator p. 244
Data types p. 248
Working with strings p. 248
Cell arrays and structures p. 249
MATLAB scripting with M-files p. 251
Plotting in MATLAB p. 252
Other useful commands and tips p. 255
Signal processing toolbox p. 258
Quick fact about the signal processing toolbox p. 258
Signal processing tool p. 262
Window design and analysis tool p. 267
Filter design toolbox p. 268
Quick fact about the filter design toolbox p. 268
Filter design and analysis tool p. 269
MATLAB functions for adaptive filtering p. 270
A case study: adaptive noise cancellation p. 272
Using MATLAB for adaptive filtering and subband adaptive filtering p. 279
Digital signal processing p. 279
Discrete-time signals and systems p. 279
Signal representations in MATLAB p. 280
Filtering and adaptive filtering in MATLAB p. 282
FIR filtering p. 282
The LMS adaptive algorithm p. 284
Anatomy of the LMS code in MATLAB p. 285
Multirate and subband adaptive filtering p. 292
Implementation of multirate filter banks p. 292
Implementation of a subband adaptive filter p. 297
Summary of MATLAB scripts, functions, examples and demos p. 301
Complexity analysis of adaptive algorithms p. 307
Index p. 317
Subband Adaptive Filtering
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