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Digital Signal and Image Processing using MATLAB, Volume 3: Advances and Applications, The Stochastic Case, 2nd Edition



Digital Signal and Image Processing using MATLAB, Volume 3: Advances and Applications, The Stochastic Case, 2nd Edition

Gérard Blanchet, Maurice Charbit

ISBN: 978-1-119-05410-8 October 2015 Wiley-ISTE 362 Pages


Volume 3 of the second edition of the fully revised and updated Digital Signal and Image Processing using MATLAB®, after first two volumes on the “Fundamentals” and “Advances and Applications: The Deterministic Case”, focuses on the stochastic case. It will be of particular benefit to readers who already possess a good knowledge of MATLAB®, a command of the fundamental elements of digital signal processing and who are familiar with both the fundamentals of continuous-spectrum spectral analysis and who have a certain mathematical knowledge concerning Hilbert spaces.

This volume is focused on applications, but it also provides a good presentation of the principles. A number of elements closer in nature to statistics than to signal processing itself are widely discussed. This choice comes from a current tendency of signal processing to use techniques from this field.

More than 200 programs and functions are provided in the MATLAB® language, with useful comments and guidance, to enable numerical experiments to be carried out, thus allowing readers to develop a deeper understanding of both the theoretical and practical aspects of this subject.

Foreword ix

Notations and Abbreviations xiii

1 Mathematical Concepts 1

1.1 Basic concepts on probability 1

1.2 Conditional expectation 9

1.3 Projection theorem 10

1.4 Gaussianity 13

1.5 Random variable transformation 18

1.6 Fundamental statistical theorems 21

1.7 Other important probability distributions 23

2 Statistical Inferences 25

2.1 Statistical model 25

2.2 Hypothesis tests 27

2.3 Statistical estimation 41

3 Monte-Carlo Simulation 85

3.1 Fundamental theorems 85

3.2 Stating the problem 86

3.3 Generating random variables 88

3.4 Variance reduction 99

4 Second Order Stationary Process 107

4.1 Statistics for empirical correlation 107

4.2 Linear prediction of WSS processes 111

4.3 Non-parametric spectral estimation of WSS processes 124

5 Inferences on HMM 139

5.1 Hidden Markov Models (HMM) 130

5.2 Inferences on HMM 142

5.3 Gaussian linear case: the Kalman filter 143

5.4 Discrete finite Markov case 152

6 Selected Topics 163

6.1 High resolution methods 163

6.2 Digital Communications 186

6.3 Linear equalization and the Viterbi algorithm 211

6.4 Compression 220

7 Hints and Solutions 235

H1 Mathematical concepts 235

H2 Statistical inferences 237

H3 Monte-Carlo simulation 269

H4 Second order stationary process 283

H5 Inferences on HMM 283

H6 Selected Topics 300

8 Appendices 317

A1 Miscellaneous functions 317

A2 Statistical functions 318

Bibliography 329

Index 333