Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing (Artech House Signal Processing Library)

ABOUT THE AUTHORS......Page 9
CONTENTS......Page 10
ORGANIZATION OF THE BOOK......Page 17
THEORYAND PRACTICE......Page 18
1.1 RANDOM SIGNALS......Page 19
1.2 SPECTRAL ESTIMATION......Page 26
1.3 SIGNAL MODELING......Page 29
1.4 ADAPTIVE FILTERING......Page 34
1.4.2 Features of Adaptive Filters......Page 41
1.5 ARRAY PROCESSING......Page 43
1.6 ORGANIZATION OF THE BOOK......Page 47
2.1 DISCRETE-TIME SIGNALS......Page 51
2.1.3 Real-World Signals......Page 54
2.2 TRANSFORM-DOMAIN REPRESENTATION OF DETERMINISTIC SIGNALS......Page 55
2.3 DISCRETE-TIME SYSTEMS......Page 65
2.4 MINIMUM PHASE AND SYSTEM INVERTIBILITY......Page 72
2.5 LATTICE FILTER REALIZATIONS......Page 82
PROBLEMS......Page 88
3.1 RANDOM VARIABLES......Page 93
3.2 RANDOM VECTORS......Page 101
3.3 DISCRETE-TIME STOCHASTIC PROCESSES......Page 115
3.4 LINEAR SYSTEMS WITH STATIONARY RANDOM INPUTS......Page 133
3.5 WHITENINGAND INNOVATIONS REPRESENTATION......Page 143
3.6 PRINCIPLES OF ESTIMATION THEORY......Page 151
3.7 SUMMARY......Page 160
PROBLEMS......Page 161
4.1 INTRODUCTION......Page 167
4.2 ALL-POLE MODELS......Page 174
4.3 ALL-ZERO MODELS......Page 190
4.4 POLE-ZERO MODELS......Page 195
4.5 MODELS WITH POLES ON THE UNIT CIRCLE......Page 200
4.6 CEPSTRUM OF POLE-ZERO MODELS......Page 202
PROBLEMS......Page 207
5 Nonparametric Power Spectrum Estimation......Page 213
5.1 SPECTRAL ANALYSIS OF DETERMINISTIC SIGNALS......Page 214
5.2 ESTIMATION OF THE AUTOCORRELATION OF STATIONARY RANDOM SIGNALS......Page 227
5.3 ESTIMATION OF THE POWER SPECTRUM OF STATIONARY RANDOM SIGNALS......Page 230
5.4 JOINT SIGNAL ANALYSIS......Page 255
5.5 MULTITAPER POWER SPECTRUM ESTIMATION......Page 264
5.6 SUMMARY......Page 272
PROBLEMS......Page 273
6.1 OPTIMUM SIGNAL ESTIMATION......Page 279
6.2 LINEAR MEAN SQUARE ERROR ESTIMATION......Page 282
6.3 SOLUTION OF THE NORMAL EQUATIONS......Page 292
6.4 OPTIMUM FINITE IMPULSE RESPONSE FILTERS......Page 296
6.5 LINEAR PREDICTION......Page 304
6.6 OPTIMUM INFINITE IMPULSE RESPONSE FILTERS......Page 313
6.7 INVERSE FILTERING AND DECONVOLUTION......Page 324
6.8 CHANNEL EQUALIZATION IN DATA TRANSMISSION SYSTEMS......Page 328
6.9 MATCHED FILTERS AND EIGENFILTERS......Page 337
PROBLEMS......Page 343
7 Algorithms and Structures for Optimum Linear Filters......Page 351
7.1 FUNDAMENTALS OF ORDER-RECURSIVE ALGORITHMS......Page 352
7.2 INTERPRETATIONS OF ALGORITHMIC QUANTITIES......Page 361
7.3 ORDER-RECURSIVE ALGORITHMS FOR OPTIMUM FIR FILTERS......Page 365
7.4 ALGORITHMS OF LEVINSON AND LEVINSON-DURBIN......Page 373
7.5 LATTICE STRUCTURES FOR OPTIMUM FIR FILTERS AND PREDICTORS......Page 379
7.6 ALGORITHM OF SCHÜR......Page 386
7.7 TRIANGULARIZATION AND INVERSION OF TOEPLITZ MATRICES......Page 392
7.8 KALMAN FILTER ALGORITHM......Page 396
7.9 SUMMARY......Page 405
PROBLEMS......Page 407
8.1 THE PRINCIPLE OF LEAST SQUARES......Page 413
8.2 LINEAR LEAST-SQUARES ERROR ESTIMATION......Page 414
8.3 LEAST-SQUARES FIR FILTERS......Page 424
8.4 LINEAR LEAST-SQUARES SIGNAL ESTIMATION......Page 429
8.5 LS COMPUTATIONS USING THE NORMAL EQUATIONS......Page 434
8.6 LS COMPUTATIONS USING ORTHOGONALIZATION TECHNIQUES......Page 440
8.7 LS COMPUTATIONS USING THE SINGULAR VALUE DECOMPOSITION......Page 449
8.8 SUMMARY......Page 456
PROBLEMS......Page 457
9.1 THE MODELING PROCESS: THEORY AND PRACTICE......Page 463
9.2 ESTIMATION OF ALL-POLE MODELS......Page 467
9.3 ESTIMATION OF POLE-ZERO MODELS......Page 480
9.4 APPLICATIONS......Page 485
9.5 MINIMUM-VARIANCE SPECTRUM ESTIMATION......Page 489
9.6 HARMONIC MODELS AND FREQUENCY ESTIMATION TECHNIQUES......Page 496
9.7 SUMMARY......Page 511
PROBLEMS......Page 512
10 Adaptive Filters......Page 517
10.1 TYPICALAPPLICATIONS OFADAPTIVE FILTERS......Page 518
10.2 PRINCIPLES OF ADAPTIVE FILTERS......Page 524
10.3 METHOD OF STEEPEST DESCENT......Page 534
10.4 LEAST-MEAN-SQUARE ADAPTIVE FILTERS......Page 542
10.5 RECURSIVE LEAST-SQUARES ADAPTIVE FILTERS......Page 566
10.6 RLS ALGORITHMS FOR ARRAY PROCESSING......Page 578
10.7 FAST RLS ALGORITHMS FOR FIR FILTERING......Page 591
10.8 TRACKING PERFORMANCE OF ADAPTIVE ALGORITHMS......Page 608
10.9 SUMMARY......Page 625
PROBLEMS......Page 626
11 Array Processing......Page 639
11.1 ARRAY FUNDAMENTALS......Page 640
11.2 CONVENTIONAL SPATIAL FILTERING: BEAMFORMING......Page 649
11.3 OPTIMUM ARRAY PROCESSING......Page 659
11.4 PERFORMANCE CONSIDERATIONS FOR OPTIMUM BEAMFORMERS......Page 670
11.5 ADAPTIVE BEAMFORMING......Page 677
11.6 OTHER ADAPTIVE ARRAY PROCESSING METHODS......Page 689
11.7 ANGLE ESTIMATION......Page 696
11.8 SPACE-TIME ADAPTIVE PROCESSING......Page 701
11.9 SUMMARY......Page 703
PROBLEMS......Page 704
12.1 HIGHER-ORDER STATISTICS IN SIGNAL PROCESSING......Page 709
12.2 BLIND DECONVOLUTION......Page 715
12.3 UNSUPERVISED ADAPTIVE FILTERS—BLIND EQUALIZERS......Page 720
12.4 FRACTIONALLY SPACED EQUALIZERS......Page 727
12.5 FRACTIONAL POLE-ZERO SIGNAL MODELS......Page 734
12.6 SELF-SIMILAR RANDOM SIGNAL MODELS......Page 743
12.7 SUMMARY......Page 759
PROBLEMS......Page 760
APPENDIX A: Matrix Inversion Lemma......Page 763
B.1 GRADIENT......Page 765
B.2 LAGRANGE MULTIPLIERS......Page 767
APPENDIX C: Matlab Functions......Page 771
D.1 COMPLEX-VALUED VECTOR SPACE......Page 773
D.2 MATRICES......Page 774
D.3 DETERMINANT OF A SQUARE MATRIX......Page 778
D.4 UNITARY MATRICES......Page 780
D.5 POSITIVE DEFINITE MATRICES......Page 782
APPENDIX E: Minimum Phase Test for Polynomials......Page 784
Bibliography......Page 787
Index......Page 805