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E-raamat: Digital Signal and Image Processing using MATLAB, Volume 3: Advances and Applications, The Stochastic Case

Gérard Blanchet, Maurice Charbit (Ecole Nationale Supérieure des Télécommunications, Paris, France)

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Ilmumisaeg: 02-Oct-2015
Kirjastus: ISTE Ltd and John Wiley & Sons Inc
Keel: eng
ISBN-13: 9781119054092

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Formaat: PDF+DRM
Ilmumisaeg: 02-Oct-2015
Kirjastus: ISTE Ltd and John Wiley & Sons Inc
Keel: eng
ISBN-13: 9781119054092

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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

Notations and Abbreviations

xiii

1 Mathematical Concepts

(24)

1.1 Basic concepts on probability

(8)

1.2 Conditional expectation

(1)

1.3 Projection theorem

(3)

1.4 Gaussianity

(5)

1.5 Random variable transformation

(3)

1.5.1 Change of variable formula

(1)

1.5.2 δ-method

(2)

1.6 Fundamental statistical theorems

(2)

1.7 Other important probability distributions

(2)

2 Statistical Inferences

(60)

2.1 Statistical model

(2)

2.2 Hypothesis tests

(14)

2.2.1 Simple hypotheses

(5)

2.2.2 Generalized Likelihood Ratio Test (GLRT)

(6)

2.2.3 Χ2 goodness of fit test

(2)

2.3 Statistical estimation

(44)

2.3.1 General principles

(2)

2.3.2 Least squares method

(1)

2.3.3 Least squares method: linear model

(12)

2.3.4 Method of moments

(3)

2.3.5 Maximum likelihood

(16)

2.3.6 Estimating a distribution

(4)

2.3.7 Bootstrap and others

(6)

3 Monte-Carlo Simulation

(22)

3.1 Fundamental theorems

(1)

3.2 Stating the problem

(2)

3.3 Generating random variables

(11)

3.3.1 The cumulative function inversion method

(2)

3.3.2 The variable transformation method

(2)

3.3.3 Acceptance-rejection method

(2)

3.3.4 Sequential methods

(4)

3.4 Variance reduction

(8)

3.4.1 Importance sampling

(4)

3.4.2 Stratification

103

(3)

3.4.3 Antithetic variates

106

(1)

4 Second Order Stationary Process

107

(32)

4.1 Statistics for empirical correlation

107

(4)

4.2 Linear prediction of WSS processes

111

(13)

4.2.1 Yule-Walker equations

111

(4)

4.2.2 Levinson-Durbin algorithm

115

(5)

4.2.3 Reflection coefficients and lattice filters

120

(4)

4.3 Non-parametric spectral estimation of WSS processes

124

(15)

4.3.1 Correlogram

125

(1)

4.3.2 Periodogram

125

(3)

4.3.3 Smoothed periodograms

128

(7)

4.3.4 Coherence

135

(4)

5 Inferences on HMM

139

(24)

5.1 Hidden Markov Models (HMM)

139

(3)

5.2 Inferences on HMM

142

(1)

5.3 Gaussian linear case: the Kalman filter

143

(9)

5.4 Discrete finite Markov case

152

(11)

5.4.1 Forward-backward formulas

153

(2)

5.4.2 Smoothing with one instant

155

(1)

5.4.3 Smoothing with two instants

156

(1)

5.4.4 HMM learning using the EM algorithm

156

(2)

5.4.5 The Viterbi algorithm

158

(5)

6 Selected Topics

163

(72)

6.1 High resolution methods

163

(23)

6.1.1 Estimating the fundamental of periodic signals: MUSIC

163

(14)

6.1.2 Introduction to array processing: MUSIC, ESPRIT

177

(9)

6.2 Digital Communications

186

(25)

6.2.1 Introduction

186

(3)

6.2.2 8-phase shift keying (PSK)

189

(2)

6.2.3 PAM modulation

191

(2)

6.2.4 Spectrum of a digital signal

193

(5)

6.2.5 The Nyquist criterion in digital communications

198

(6)

6.2.6 The eye pattern

204

(1)

6.2.7 PAM modulation on the Nyquist channel

205

(6)

6.3 Linear equalization and the Viterbi algorithm

211

(9)

6.3.1 Linear equalization

213

(2)

6.3.2 The soft decoding Viterbi algorithm

215

(5)

6.4 Compression

220

(15)

6.4.1 Scalar Quantization

220

(2)

6.4.2 Vector Quantization

222

(13)

7 Hints and Solutions

235

(82)

H1 Mathematical concepts

235

(2)

H2 Statistical inferences

237

(32)

H3 Monte-Carlo simulation

269

(8)

H4 Second order stationary process

277

(6)

H5 Inferences on HMM

283

(17)

7.6 Selected Topics

300

(17)

8 Appendices

317

(12)

A1 Miscellaneous functions

317

(1)

A2 Statistical functions

318

(11)

A.2.1 Notable functions

318

(1)

A.2.2 Beta distribution

318

(1)

A.2.3 Student's distribution

318

(5)

A.2.4 Chi-squared distribution

323

(3)

A.2.5 Fisher's distribution

326

(3)

Bibliography

329

(4)

Index

333

Gérard Blanchet is Professor at Telecom ParisTech, France. In addition to his research, teaching and consulting activities, he is the author of several books on automatic control systems, digital signal processing and computer architecture. He also develops tools and methodologies to improve knowledge acquisition in various fields.

Maurice Charbit is Professor at Telecom ParisTech, France. He is a teacher in probability theory, signal processing, communication theory and statistics for data processing. With regard to research, his main areas of interest are: (i) the Bayesian approach for hidden Markov models, (ii) the 3D model-based approach for face tracking, and (iii) processing for multiple sensor arrays with applications to infrasonic systems.

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