Subband Adaptive Filtering: Theory and Implementation

Subband Adaptive Filtering......Page 5
Contents......Page 7
About the authors......Page 13
Preface......Page 15
Acknowledgments......Page 17
List of symbols......Page 19
List of abbreviations......Page 21
1.1 Adaptive filtering......Page 23
1.2 Adaptive transversal filters......Page 24
1.3 Performance surfaces......Page 26
1.4 Adaptive algorithms......Page 28
1.5 Spectral dynamic range and misadjustment......Page 35
1.6.1 Adaptive system identification......Page 37
1.6.2 Adaptive prediction......Page 45
1.6.3 Adaptive inverse modeling......Page 47
1.6.4 Adaptive array processing......Page 50
1.7.1 Transform-domain adaptive filters......Page 53
1.7.2 Subband adaptive filters......Page 60
References......Page 61
2.1 Multirate systems......Page 63
2.2 Filter banks......Page 66
2.2.1 Input–output relation......Page 68
2.2.2 Perfect reconstruction filter banks......Page 69
2.2.3 Polyphase representation......Page 70
2.3 Paraunitary filter banks......Page 76
2.4.1 Filter bank as a block transform......Page 77
2.5 Cosine-modulated filter banks......Page 81
2.5.1 Design example......Page 85
2.6 DFT filter banks......Page 87
2.6.1 Design example......Page 88
2.7 A note on cosine modulation......Page 89
2.8 Summary......Page 90
References......Page 91
3.1 Correlation-domain formulation......Page 95
3.1.1 Critical decimation......Page 99
3.2 Cross spectrum......Page 101
3.2.1 Subband spectrum......Page 104
3.3 Orthogonality at zero lag......Page 107
3.3.1 Paraunitary condition......Page 108
3.4.1 Correlation-domain analysis......Page 111
3.4.2 MATLAB simulations......Page 114
3.5 Summary......Page 118
References......Page 119
4.1 Subband adaptive filtering......Page 121
4.1.1 Computational reduction......Page 122
4.1.2 Spectral dynamic range......Page 123
4.2.2 Closed-loop structures......Page 126
4.3 Aliasing, band-edge effects and solutions......Page 128
4.3.1 Aliasing and band-edge effects......Page 129
4.3.2 Adaptive cross filters......Page 130
4.3.3 Multiband-structured SAF......Page 132
4.3.4 Closed-loop delayless structures......Page 135
4.4.1 Closed-loop configuration......Page 136
4.4.2 Open-loop configuration......Page 137
4.4.3 Weight transformation......Page 138
4.4.4 Computational requirements......Page 145
4.5 MATLAB examples......Page 146
4.5.1 Aliasing and band-edge effects......Page 147
4.5.2 Delayless alias-free SAFs......Page 148
4.6 Summary......Page 150
References......Page 151
5.1 Variants of critically sampled subband adaptive filters......Page 155
5.1.1 SAF with the affine projection algorithm......Page 156
5.1.2 SAF with variable step sizes......Page 158
5.1.3 SAF with selective coefficient update......Page 159
5.2.1 Oversampled subband adaptive filtering......Page 160
5.2.2 Nonuniform subband adaptive filtering......Page 162
5.3.1 Generalized DFT filter banks......Page 163
5.3.2 Single-sideband modulation filter banks......Page 164
5.3.3 Filter design criteria for DFT filter banks......Page 166
5.3.4 Quadrature mirror filter banks......Page 171
5.3.5 Pseudo-quadrature mirror filter banks......Page 175
5.3.6 Conjugate quadrature filter banks......Page 177
5.4.1 Multiband structure with proportionate adaptation......Page 178
5.4.2 MATLAB simulations......Page 179
5.5 Summary......Page 183
References......Page 185
6.1 Multiband structure......Page 189
6.1.1 Polyphase implementation......Page 192
6.2.2 Constrained subband updates......Page 195
6.2.3 Computational complexity......Page 197
6.3 Underdetermined least-squares solutions......Page 199
6.3.1 NLMS equivalent......Page 200
6.4.1 Stochastic approximation to Newton’s method......Page 201
6.4.2 Weighted MSE criterion......Page 203
6.4.3 Decorrelating properties......Page 208
6.5.2 Power complementary filter bank......Page 209
6.5.3 The number of subbands......Page 210
6.6.1 Open-loop configuration......Page 211
6.6.2 Closed-loop configuration......Page 213
6.7 MATLAB examples......Page 214
6.7.1 Convergence of the MSAF algorithm......Page 215
6.7.2 Subband and time-domain constraints......Page 217
6.8 Summary......Page 220
References......Page 221
7.1.1 The MSAF algorithm......Page 225
7.1.2 Linear data model......Page 226
7.1.3 Paraunitary filter banks......Page 228
7.2.1 MSE functions......Page 231
7.2.2 Excess MSE......Page 232
7.3.1 Projection interpretation......Page 233
7.3.2 Mean behavior......Page 235
7.4.1 Energy conservation relation......Page 236
7.4.3 Stability of the MSAF algorithm......Page 238
7.4.4 Steady-state excess MSE......Page 239
7.5.1 Mean of the projection matrix......Page 241
7.5.2 Stability bounds......Page 242
7.5.3 Steady-state excess MSE......Page 244
7.6 Summary......Page 245
References......Page 246
8.1 Recent research on filter bank design......Page 249
8.2.1 In-band aliasing cancellation......Page 250
8.2.3 Variable tap lengths for the SAF......Page 252
8.4 Applications of the SAF......Page 254
8.5 Further research on a multiband-structured SAF......Page 255
8.6 Concluding remarks......Page 256
References......Page 257
A.1.1 Starting MATLAB......Page 263
A.1.3 The colon operator......Page 266
A.1.5 Working with strings......Page 270
A.1.6 Cell arrays and structures......Page 271
A.1.7 MATLAB scripting with M-files......Page 273
A.1.8 Plotting in MATLAB......Page 274
A.1.9 Other useful commands and tips......Page 277
A.2.1 Quick fact about the signal processing toolbox......Page 280
A.2.2 Signal processing tool......Page 284
A.2.3 Window design and analysis tool......Page 289
A.3.1 Quick fact about the filter design toolbox......Page 290
A.3.2 Filter design and analysis tool......Page 291
A.3.3 MATLAB functions for adaptive filtering......Page 292
A.3.4 A case study: adaptive noise cancellation......Page 294
B.1.1 Discrete-time signals and systems......Page 301
B.1.2 Signal representations in MATLAB......Page 302
B.2.1 FIR filtering......Page 304
B.2.2 The LMS adaptive algorithm......Page 306
B.2.3 Anatomy of the LMS code in MATLAB......Page 307
B.3.1 Implementation of multirate filter banks......Page 314
B.3.2 Implementation of a subband adaptive filter......Page 319
Appendix C Summary of MATLAB scripts, functions, examples and demos......Page 323
Appendix D Complexity analysis of adaptive algorithms......Page 329
Index......Page 339