Optimum signal processing

Preface......Page 10
Preface to the First Edition......Page 12
1.1 Probability Density, Mean, Variance......Page 16
1.2 Chebyshev’s Inequality......Page 17
1.3 Joint and Conditional Densities, and Bayes’ Rule......Page 19
1.4 Correlation Canceling......Page 22
1.5 Gram-Schmidt Orthogonalization......Page 26
1.6 Partial Correlations......Page 34
1.7 Forward/Backward Prediction and LU/UL Factorization......Page 38
1.8 Random Signals......Page 53
1.9 Power Spectrum and Its Interpretation......Page 55
1.10 Sample Autocorrelation and the Periodogram......Page 57
1.11 Random Signal Models and Their Uses......Page 60
1.12 Filter Model of First Order Autoregressive Process......Page 66
1.13 Stability and Stationarity......Page 67
1.14 Parameter Estimation by the Maximum Likelihood Method......Page 68
1.15 Parameter Estimation by the Yule-Walker Method......Page 69
1.16 Linear Prediction and Signal Modeling......Page 71
1.17 Cramer–Rao Bound and Maximum Likelihood......Page 73
1.18 Problems......Page 78
1.19 References......Page 85
2.1 Filtering of Stationary Random Signals......Page 87
2.2 System Identification by Cross-Correlation Methods......Page 90
2.3 Noise Reduction and Signal Enhancement Filters......Page 91
2.4 Quantization Noise......Page 98
2.5 Statistical Treatment of Multiplier Roundoff Error......Page 99
2.6 Introduction to Linear Prediction......Page 101
2.7 Gapped Functions, Levinson and Schur Recursions......Page 106
2.8 Introduction to Data Compression and DPCM......Page 112
2.9 Problems......Page 115
2.10 References......Page 119
3.1 Minimum-Phase Signals and Filters......Page 121
3.2 Partial Energy and Minimal Delay......Page 122
3.4 Minimum-Delay Property......Page 123
3.5 Minimum-Phase Property......Page 124
3.6 Spectral Factorization Theorem......Page 125
3.7 Minimum-Phase Property of the Prediction-Error Filter......Page 127
3.8 Problems......Page 128
3.9 References......Page 130
4 Linear Estimation of Signals......Page 132
4.1 Linear and Nonlinear Estimation of Signals......Page 133
4.2 Orthogonality and Normal Equations......Page 136
4.3 Stationary Wiener Filter......Page 140
4.4 Construction of the Wiener Filter by Prewhitening......Page 142
4.5 Wiener Filter Example......Page 144
4.6 Wiener Filter as Kalman Filter......Page 145
4.7 Construction of the Wiener Filter by the Gapped Function......Page 150
4.8 Construction of the Wiener Filter by Covariance Factorization......Page 151
4.9 The Kalman Filter......Page 154
4.10 Problems......Page 157
4.11 References......Page 160
5.1 Pure Prediction and Signal Modeling......Page 162
5.2 Autoregressive Models......Page 165
5.3 Linear Prediction and the Levinson Recursion......Page 167
5.4 Levinson’s Algorithm in Matrix Form......Page 175
5.5 Autocorrelation Sequence Extensions......Page 179
5.6 Split Levinson Algorithm......Page 182
5.7 Analysis and Synthesis Lattice Filters......Page 185
5.8 Alternative Proof of the Minimum-Phase Property......Page 189
5.9 Orthogonality of Backward Prediction Errors—Cholesky Factorization......Page 191
5.10 Schur Algorithm......Page 195
5.11 Lattice Realizations of FIR Wiener Filters......Page 201
5.12 Autocorrelation, Covariance, and Burg’s Methods......Page 208
5.13 Dynamic Predictive Deconvolution—Waves in Layered Media......Page 213
5.14 Least-Squares Waveshaping and Spiking Filters......Page 226
5.15 Problems......Page 236
5.16 References......Page 242
6.1 Spectrum Estimation by Autoregressive Modeling......Page 249
6.2 Spectral Analysis of Sinusoids in Noise......Page 251
6.3 Superresolution Array Processing......Page 263
6.4 Eigenvector Methods......Page 274
6.5 MUSIC method......Page 276
6.6 Minimum-Norm Method......Page 279
6.7 Reduced-Order Method......Page 282
6.8 Maximum Likelihood Method......Page 285
6.9 ESPRIT Method......Page 286
6.10 Spatial Smoothing......Page 288
6.11 Asymptotic Properties......Page 291
6.12 Problems......Page 299
6.13 References......Page 305
7.1 Adaptive Implementation of Wiener Filters......Page 312
7.2 Correlation Canceler Loop (CCL)......Page 315
7.3 The Widrow-Hoff LMS Adaptation Algorithm......Page 317
7.4 Adaptive Linear Combiner......Page 321
7.5 Adaptive FIR Wiener Filter......Page 323
7.6 Speed of Convergence......Page 326
7.7 Adaptive Channel Equalizers......Page 329
7.8 Adaptive Echo Cancelers......Page 330
7.9 Adaptive Noise Canceling......Page 331
7.10 Adaptive Line Enhancer......Page 333
7.11 Adaptive Linear Prediction......Page 335
7.12 Adaptive Implementation of Pisarenko’s Method......Page 337
7.13 Gradient Adaptive Lattice Filters......Page 342
7.14 Adaptive Gram-Schmidt Preprocessors......Page 349
7.15 Rank-One Modification of Covariance Matrices......Page 354
7.16 RLS Adaptive Filters......Page 365
7.17 Fast RLS Filters......Page 368
7.18 RLS Lattice Filters......Page 371
7.19 Problems......Page 376
7.20 References......Page 380
8.1 Fortran and C Functions......Page 387
8.2 MATLAB Functions......Page 388
Index......Page 389