Adaptive Digital Filters

Contents......Page 0
Adaptive Digital Filters Second Edition, Revised and Expanded......Page 1
Signal Processing and Communications......Page 3
Preface......Page 7
Contents......Page 9
Adaptive Filtering and Signal Analysis......Page 10
1.1. SIGNAL ANALYSIS......Page 11
1.2. CHARACTERIZATION AND MODELING......Page 13
1.3. ADAPTIVE FILTERING......Page 15
1.4. NORMAL EQUATIONS......Page 17
1.5. RECURSIVE ALGORITHMS......Page 18
1.6. IMPLEMENTATION AND APPLICATIONS......Page 20
REFERENCES......Page 22
REFERENCES......Page 65
2.1. THE DAMPED SINUSOID......Page 24
2.2. PERIODIC SIGNALS......Page 27
2.3. RANDOM SIGNALS......Page 31
2.4. GAUSSIAN SIGNALS......Page 34
2.5. SYNTHETIC, MOVING AVERAGE, AND AUTOREGRESSIVE SIGNALS......Page 35
2.6. ARMA SIGNALS......Page 41
2.7. MARKOV SIGNALS......Page 46
2.8. LINEAR PREDICTION AND INTERPOLATION......Page 48
2.9. PREDICTABLE SIGNALS......Page 51
2.10. THE FUNDAMENTAL (WOLD) DECOMPOSITION......Page 53
2.11. HARMONIC DECOMPOSITION......Page 55
2.12. MULTIDIMENSIONAL SIGNALS......Page 57
2.13. NONSTATIONARY SIGNALS......Page 59
2.14. NATURAL SIGNALS......Page 60
2.15. SUMMARY......Page 61
EXERCISES......Page 63
3.1. CROSS-CORRELATION AND AUTOCORRELATION......Page 66
3.2. ESTIMATION OF CORRELATION FUNCTIONS......Page 69
3.3. RECURSIVE ESTIMATION......Page 75
3.4. THE AUTOCORRELATION MATRIX......Page 77
3.5. SOLVING LINEAR EQUATION SYSTEMS......Page 79
3.6. EIGENVALUE DECOMPOSITION......Page 81
3.7. EIGENFILTERS......Page 85
3.8. PROPERTIES OF EXTREMAL EIGENVALUES......Page 89
3.9. SIGNAL SPECTRUM AND EIGENVALUES......Page 91
3.10. ITERATIVE DETERMINATION OF EXTREMAL EIGENPARAMETERS......Page 93
3.11. ESTIMATION OF THE AC MATRIX......Page 95
3.12. EIGEN (KL) TRANSFORM AND APPROXIMATIONS......Page 98
EXERCISES......Page 101
SYSTEM WITH SYMMETRICAL MATRIX......Page 103
ANNEX 3.2 FORTRAN SUBROUTINE TO COMPUTE THE EIGENVECTOR CORRESPONDING TO THE MINIMUM EIGENVALUE BY THE CONJUGATE GRADIENT METHOD [20]......Page 104
REFERENCES......Page 108
4.1. THE GRADIENT—LMS ALGORITHM......Page 110
4.2. STABILITY CONDITION AND SPECIFICATIONS......Page 111
4.3. RESIDUAL ERROR......Page 113
4.4. LEARNING CURVE AND TIME CONSTANT......Page 117
4.5. WORD-LENGTH LIMITATIONS......Page 119
4.6. LEAKAGE FACTOR......Page 125
4.7. THE LMAV AND SIGN ALGORITHMS......Page 126
4.8. NORMALIZED ALGORITHMS FOR NONSTATIONARY SIGNALS......Page 130
4.9. DELAYED LMS ALGORITHMS......Page 135
4.10. THE MOMENTUM ALGORITHM......Page 137
4.12. CONSTRAINED LMS ALGORITHMS......Page 138
4.13. THE BLOCK LMS ALGORITHM......Page 140
4.14. FIR FILTERS IN CASCADE FORM......Page 141
4.15. IIR GRADIENT ADAPTIVE FILTERS......Page 143
4.16. NONLINEAR FILTERING......Page 146
EXERCISES......Page 149
REFERENCES......Page 151
5.1. DEFINITION AND PROPERTIES......Page 153
5.2. FIRST- AND SECOND-ORDER FIR PREDICTORS......Page 156
5.3. FORWARD AND BACKWARD PREDICTION EQUATIONS......Page 157
5.4. ORDER ITERATIVE RELATIONS......Page 160
5.5. THE SPLIT LEVINSON ALGORITHM......Page 163
5.6. THE LATTICE LINEAR PREDICTION FILTER......Page 165
5.7. THE INVERSE AC MATRIX......Page 168
5.8. THE NOTCH FILTER AND ITS APPROXIMATION......Page 170
5.9. ZEROS OF FIR PREDICTION ERROR FILTERS......Page 172
5.10. POLES OF IIR PREDICTION ERROR FILTERS......Page 175
5.11. GRADIENT ADAPTIVE PREDICTORS......Page 177
5.12. ADAPTIVE LINEAR PREDICTION OF SINUSOIDS......Page 182
5.13. LINEAR PREDICTION AND HARMONIC DECOMPOSITION......Page 185
5.14. ITERATIVE DETERMINATION OF THE RECURRENCE COEFFICIENTS OF A PREDICTABLE SIGNAL......Page 187
5.15. CONCLUSION......Page 191
EXERCISES......Page 192
ANNEX 5.1 LEVINSON ALGORITHM......Page 194
REFERENCES......Page 195
6.1. THE FIRST-ORDER LS ADAPTIVE FILTER......Page 197
6.2. RECURSIVE EQUATIONS FOR THE ORDER N FILTER......Page 201
6.3. RELATIONSHIPS BETWEEN LS VARIABLES......Page 204
6.4. FAST ALGORITHM BASED ON A PRIORI ERRORS......Page 208
6.5. ALGORITHM BASED ON ALL PREDICTION ERRORS......Page 211
6.6. STABILITY CONDITIONS FOR LS RECURSIVE ALGORITHMS......Page 216
6.7. INITIAL VALUES OF THE PREDICTION ERROR ENERGIES......Page 218
6.8. BOUNDING PREDICTION ERROR ENERGIES......Page 219
6.9. ROUNDOFF ERROR ACCUMULATION AND ITS CONTROL......Page 222
6.10. A SIMPLIFIED ALGORITHM......Page 224
6.11. PERFORMANCE OF LS ADAPTIVE FILTERS......Page 225
6.12. SELECTING FLS PARAMETER VALUES......Page 230
6.13. WORD-LENGTH LIMITATIONS AND IMPLEMENTATION......Page 233
6.14. COMPARISON OF FLS AND LMS APPROACHES—SUMMARY......Page 234
EXERCISES......Page 237
ANNEX 6.1 FLS ALGORITHM BASED ON A PRIORI ERRORS......Page 238
ANNEX 6.2 FLS ALGORITHM BASED ON ALL THE PREDICTION ERRORS AND WITH ROUNDOFF ERROR CONTROL (SIMPLEST VERSION)......Page 239
REFERENCES......Page 241
7.1. COVARIANCE ALGORITHMS......Page 242
7.2. A SLIDING WINDOW ALGORITHM......Page 245
7.3. ALGORITHMS WITH VARIABLE WEIGHTING FACTORS......Page 251
7.4. FORWARD–BACKWARD LINEAR PREDICTION......Page 254
7.5. LINEAR PHASE ADAPTIVE FILTERING......Page 258
7.6. CONSTRAINED ADAPTIVE FILTERING......Page 260
7.7. A ROBUST CONSTRAINED ALGORITHM......Page 262
7.8. THE CASE OF COMPLEX SIGNALS......Page 266
7.9. MULTIDIMENSIONAL INPUT SIGNALS......Page 268
7.10. M-D ALGORITHM BASED ON ALL PREDICTION ERRORS......Page 273
7.11. FILTERS OF NONUNIFORM LENGTH......Page 276
7.13. MULTIRATE ADAPTIVE FILTERS......Page 279
7.12. FLS POLE-ZERO MODELING......Page 277
7.14. FREQUENCY DOMAIN ADAPTIVE FILTERS......Page 284
7.15. SECOND-ORDER NONLINEAR FILTERS......Page 286
7.16. UNIFIED GENERAL VIEW AND CONCLUSION......Page 288
EXERCISES......Page 290
ANNEX 7.1 FLS ALGORITHM WITH SLIDING WINDOW......Page 291
ANNEX 7.2 FLS ALGORITHM FOR FORWARD– BACKWARD LINEAR PREDICTION......Page 293
ANNEX 7.3 FLS ALGORITHM WITH MULTIDIMENSIONAL INPUT SIGNAL......Page 295
REFERENCES......Page 298
8.1. ORDER RECURRENCE RELATIONS FOR PREDICTION COEFFICIENTS......Page 300
8.2. ORDER RECURRENCE RELATIONS FOR THE FILTER COEFFICIENTS......Page 303
8.3. TIME RECURRENCE RELATIONS......Page 306
8.4. FLS ALGORITHMS FOR LATTICE STRUCTURES......Page 307
8.5. NORMALIZED LATTICE ALGORITHMS......Page 310
8.6. CALCULATION OF TRANSVERSAL FILTER COEFFICIENTS......Page 314
8.7. MULTIDIMENSIONAL LATTICE ALGORITHMS......Page 317
8.8. BLOCK PROCESSING......Page 321
8.9. GEOMETRICAL DESCRIPTION......Page 322
8.10. ORDER AND TIME RECURSIONS......Page 326
8.11. UNIFIED DERIVATION OF FLS ALGORITHMS......Page 330
8.12. SUMMARY AND CONCLUSION......Page 332
EXERCISES......Page 333
ANNEX 8.1 FLS ALGORITHM FOR A PREDICTOR IN LATTICE STRUCTURE......Page 334
REFERENCES......Page 336
Rotation- Based Algorithms......Page 338
9.1. THE ROTATION OPERATION......Page 339
9.2. THE QR DECOMPOSITION......Page 340
9.3. ROTATIONS IN BACKWARD LINEAR PREDICTION......Page 342
9.4. ROTATION IN FORWARD LINEAR PREDICTION......Page 345
9.5. THE FAST LEAST SQUARES QR ALGORITHM......Page 348
9.6. IMPLEMENTATION ASPECTS......Page 350
9.7. THE CASE OF COMPLEX SIGNALS......Page 353
9.8. MULTIDIMENSIONAL SIGNALS......Page 354
9.9. NORMALIZATION AND EQUIVALENCE WITH LATTICE......Page 357
9.10. CONCLUSION......Page 358
EXERCISES......Page 359
ANNEX 9.1 FORTRAN SUBROUTINE FOR THE FLSQR ALGORITHM......Page 360
REFERENCES......Page 362
10.1. DEFINITION AND OBJECTIVES......Page 363
10.2. THE PERIODOGRAM METHOD......Page 364
10.3. THE CORRELOGRAM METHOD......Page 366
10.4. THE MINIMUM VARIANCE (MV) METHOD......Page 368
10.5. HARMONIC RETRIEVAL TECHNIQUES......Page 371
10.6. AUTOREGRESSIVE MODELING......Page 375
10.7. ARMA MODELING......Page 380
10.8. SIGNAL AND NOISE SPACE METHODS......Page 381
10.9. ESTIMATION BOUNDS......Page 384
10.10. CONCLUSION......Page 386
EXERCISES......Page 387
REFERENCES......Page 388
11.1. DIVISION AND SQUARE ROOT......Page 390
11.2. A MULTIBUS ARCHITECTURE......Page 393
11.3. LINE CANCELING AND ENHANCEMENT......Page 394
11.4. ADAPTIVE DIFFERENTIAL CODING......Page 395
11.5. ADAPTIVE DECONVOLUTION......Page 397
11.6. ADAPTIVE PROCESSING IN RADAR......Page 399
11.7. ADAPTIVE ANTENNAS......Page 400
11.8. IMAGE SIGNAL PREDICTION......Page 401
11.9. ARTIFICIAL INTELLIGENCE AND NEURAL NETWORKS......Page 402
11.10. CONCLUSION......Page 408
EXERCISES......Page 409
REFERENCES......Page 410
12.1. AUTOMATIC GAIN CONTROL......Page 411
12.2.1. Data Echo Canceller......Page 413
12.2.2. Voice Echo Canceller......Page 416
12.3.1. Channel Models......Page 418
12.3.2. The Matched Filter......Page 419
12.3.3. The Wiener Filter......Page 421
12.4. TRANSVERSAL EQUALIZER......Page 422
12.5. DECISION FEEDBACK EQUALIZER—DFE......Page 425
12.6. FRACTIONALLY SPACED EQUALIZER......Page 429
12.7. MAXIMUM-LIKELIHOOD ALGORITHMS (MLA)......Page 431
12.8. COMPARISON OF EQUALIZATION APPROACHES......Page 434
12.9. CARRIER FREQUENCY ESTIMATION......Page 436
12.10. ALGORITHMS FOR RADIO COMMUNICATIONS......Page 439
12.10.1. Zero Forcing (ZF) Algorithm......Page 440
12.10.2. The Constant Modulus Algorithm (CMA)......Page 441
12.10.3. Optimal Multipath Equalization......Page 442
12.10.4. Adaptive Antennas for Cellular Systems......Page 444
EXERCISES......Page 446
REFERENCES......Page 449