Digital Processing of Random Signals Theory and Methods

by Porat, Boaz

• ISBN13: 9780486462981
• ISBN10: 0486462986
• Format: Paperback
• Copyright: 2008-02-29
• Publisher: Dover Publications
• More Book Details

Summary

This excellent advanced text rigorously covers several topics related to random signal processing. Geared toward students of electrical engineering, its material is sufficiently general to be applicable to other engineering fields. It features numerous problems of varying difficulty, some with hints and solutions. 1994 edition.

Author Biography

Boaz Porat, Department of Electrical Engineering, Technion, Israel Institute of Technology, Haifa, Israel

Table of Contents

Preface	p. viii
Introduction	p. 1
References	p. 9
The Structure of Stationary Processes	p. 11
Discrete-time Random Processes	p. 11
Gaussian Random Processes	p. 13
Stationarity and Ergodicity	p. 13
The Covariances of Stationary Processes	p. 14
Some Examples	p. 15
Hilbert Spaces of Stationary Processes	p. 17
The Wold Decomposition	p. 21
Spectral Distributions and Spectral Densities	p. 27
Spectral Factorization	p. 33
Properties of the Best Linear Predictor	p. 34
Wide Sense Ergodicity of Gaussian Processes	p. 38
Parametric Models for Stationary Processes	p. 41
Mathematica Packages	p. 48
References	p. 49
Problems	p. 50
Parameter Estimation Theory	p. 56
Principles of Parameter Estimation	p. 56
Properties of Estimates	p. 61
Covariance Inequalities and Efficiency	p. 65
Sequences of Estimates	p. 70
Maximum Likelihood Estimation	p. 73
The Method of Moments	p. 78
Least-squares Estimation	p. 88
Maximum Entropy Estimation	p. 90
Model Order Selection	p. 91
References	p. 93
Problems	p. 94
Nonparametric Spectrum Estimation	p. 98
Introduction	p. 98
Estimation of the Mean and the Covariances	p. 100
The Periodogram	p. 106
Periodogram Averaging	p. 112
Smoothed Periodograms	p. 114
Windowed Periodograms	p. 119
Mathematica Packages	p. 127
References	p. 128
Problems	p. 129
Parameter Estimation Theory for Gaussian Processes	p. 133
Introduction	p. 133
The Fisher Information of Stationary Gaussian Processes	p. 134
Maximum Likelihood Parameter Estimation	p. 139
The Relative Efficiency of the Sample Covariances	p. 142
Parameter Estimation from the Sample Covariances	p. 144
Mathematica Packages	p. 147
References	p. 148
Problems	p. 148
Autoregressive Parameter Estimation	p. 152
The Yule-Walker Estimate	p. 152
The Levinson-Durbin Algorithm	p. 156
Algorithms Related to Levinson-Durbin	p. 163
Lattice Filters	p. 167
Maximum Entropy Estimation	p. 170
Least-squares Estimation	p. 171
Maximum Likelihood Estimation	p. 173
Estimation of the Partial Correlation Coefficients	p. 175
Model Order Selection	p. 178
Estimation of the Spectral Density	p. 179
Mathematica Packages	p. 181
References	p. 182
Problems	p. 183
Moving Average and ARMA Parameter Estimation	p. 187
Introduction	p. 187
Moving Average Parameter Estimation: Elementary Methods	p. 188
Moving Average Parameter Estimation: Advanced Methods	p. 191
ARMA Estimation: The Modified Yule-Walker Method	p. 196
ARMA Estimation from the Sample Covariances	p. 199
Approximate Maximum Likelihood ARMA Estimation	p. 202
Exact Maximum Likelihood ARMA Estimation	p. 205
An Example: EMG Signal Analysis	p. 209
Mathematica Packages	p. 211
References	p. 213
Problems	p. 215
Adaptive AR and ARMA Estimation	p. 218
Introduction	p. 218
The Recursive Least-squares Algorithm	p. 219
The Extended Least-squares Algorithm	p. 223
The Recursive Maximum Likelihood Algorithm	p. 225
Stochastic Gradient Algorithms	p. 229
Projection Operators in Euclidean Spaces	p. 231
Lattice Algorithms for Autoregressive Estimation	p. 235
Lattice Algorithms for ARMA Estimation	p. 242
Extensions of Lattice Algorithms	p. 246
Mathematica Packages	p. 252
References	p. 254
Problems	p. 255
Estimation of Deterministic Processes	p. 260
Introduction	p. 260
The Cramer-Rao Bound for Sinusoids in White Noise	p. 262
Maximum Likelihood Estimation	p. 266
The Prony Method	p. 270
The Truncated Singular Value Decomposition Method	p. 272
Estimation from the Sample Covariances	p. 277
Estimation from the Sample Covariance Matrix	p. 281
Concluding Remarks	p. 285
Mathematica Packages	p. 286
References	p. 288
Problems	p. 290
High-order Statistical Analysis	p. 294
Introduction	p. 294
Definition and Properties of Cumulants	p. 295
Cumulants and Polyspectra of Stationary Linear Processes	p. 300
The Cumulants of ARMA Processes	p. 305
Estimation of the Cumulants	p. 308
Moving Average Parameter Estimation: Linear Methods	p. 313
ARMA Parameter Estimation: Linear Methods	p. 317
MA and ARMA Parameter Estimation: Nonlinear Methods	p. 318
Deconvolution	p. 321
Estimation of Sinusoids in Gaussian Noise	p. 324
Mathematica Packages	p. 325
References	p. 327
Problems	p. 329
Time-frequency Signal Analysis: Linear Transforms	p. 332
Introduction	p. 332
The Short-time Fourier Transform	p. 335
The Gabor Representation: Elementary Discussion	p. 337
The Gabor Representation: Advanced Discussion	p. 342
The Wavelet Transform	p. 349
Orthonormal Wavelet Bases	p. 353
Implementation of Linear Transforms for Discrete-time Signals	p. 361
Mathematica Packages	p. 364
References	p. 365
Problems	p. 366
Time-frequency Signal Analysis: Nonlinear Transforms	p. 369
Introduction	p. 369
The Wigner-Ville Distribution: Part I	p. 370
The Wigner-Ville Distribution: Part II	p. 377
The Ambiguity Function	p. 383
The Cohen Class of Distributions	p. 387
High-order Ambiguity Functions	p. 392
Estimation Using the High-order Ambiguity Function	p. 397
Mathematica Packages	p. 404
References	p. 405
Problems	p. 407
Notations and Facts	p. 410
References	p. 413
Hilbert Spaces	p. 414
References	p. 420
Asymptotic Theory	p. 421
References	p. 428
Kronecker Products and Liapunov Equations	p. 429
References	p. 437
Author Index	p. 439
Subject Index	p. 443
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