Digital Processing of Random Signals / Edition 1

Digital Processing of Random Signals / Edition 1

by Boaz Porat

ISBN-10: 0130637513

ISBN-13: 9780130637512

Pub. Date: 12/28/1993

Publisher: Prentice Hall Professional Technical Reference

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.


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.

Product Details

Prentice Hall Professional Technical Reference
Publication date:
Prentice Hall Information and System Sciences Series
Product dimensions:
7.21(w) x 9.58(h) x 1.08(d)

Table of Contents

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

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