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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
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.
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Veröffentlichungsjahr: 2015
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Contents
Cover
Title
Copyright
Foreword
Notations and Abbreviations
1: Mathematical Concepts
1.1 Basic concepts on probability
1.2 Conditional expectation
1.3 Projection theorem
1.4 Gaussianity
1.5 Random variable transformation
1.6 Fundamental statistical theorems
1.7 Other important probability distributions
2: Statistical Inferences
2.1 Statistical model
2.2 Hypothesis tests
2.3 Statistical estimation
3: Monte-Carlo Simulation
3.1 Fundamental theorems
3.2 Stating the problem
3.3 Generating random variables
3.4 Variance reduction
4: Second Order Stationary Process
4.1 Statistics for empirical correlation
4.2 Linear prediction of WSS processes
4.3 Non-parametric spectral estimation of WSS processes
5: Inferences on HMM
5.1 Hidden Markov Models (HMM)
5.2 Inferences on HMM
5.3 Gaussian linear case: the Kalman filter
5.4 Discrete finite Markov case
6: Selected Topics
6.1 High resolution methods
6.2 Digital Communications
6.3 Linear equalization and the Viterbi algorithm
6.4 Compression
7: Hints and Solutions
H1 Mathematical concepts
H2 Statistical inferences
H3 Monte-Carlo simulation
H4 Second order stationary process
H5 Inferences on HMM
H6 Selected Topics
8: Appendices
A1 Miscellaneous functions
A2 Statistical functions
Bibliography
Index
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
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Cover
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Digital Signal and Image Processing using MATLAB®
Advances and Applications: The Stochastic Case
Revised and Updated 2nd Edition
Volume 3
Gérard Blanchet
Maurice Charbit
First published 2015 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2015
The rights of Gérard Blanchet and Maurice Charbit to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2015948073
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-84821-795-9
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. The book’s use or discussion of MATLAB® software does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or use of the MATLAB® software.
Foreword
This book is the third volume in a series on digital signal processing and associated techniques. Following on from “Fundamentals” and “Advances and Applications, The Deterministic Case”, it addresses the stochastic case. We shall presume throughout that readers have a good working knowledge of MATLAB® and of basic elements of digital signal processing.
Whilst our main focus is on applications, we shall also give consideration to key principles. A certain number of the elements discussed belong more to the domain of statistics than to signal processing; this responds to current trends in signal processing, which make extensive use of this type of technique.
Over 60 solved exercises allow the reader to apply the concepts and results presented in the following chapters. There will also be examples to alleviate any demonstrations that would otherwise be quite dense. These can be found in more specialist books referenced in the bibliography. 92 programs and 49 functions will be used to support these examples and corrected exercises.
Mathematical Concepts
The first chapter begins with a brief review of probability theory, focusing on the notions of conditional probability, projection theorem and random variable transformation. A number of statistical elements will also be presented, including the law of large numbers (LLN), the limit-central theorem, or the delta-method.
Statistical inferences
The second chapter is devoted to statistical inference. Statistical inference consists of deducing interesting characteristics from a series of observations with a certain degree of reliability. A variety of techniques may be used. In this chapter, we shall discuss three broad families of techniques: hypothesis testing, parameter estimation, and the determination of confidence intervals. Key notions include Cramer-Rao bound, likelihood ratio tests, maximum likelihood approach and least square approach for linear models.
Monte-Carlo simulation
Monte-Carlo methods involve a set of algorithms which aim to calculate values using a pseudo-random generator. The quantities to calculate are typically integrals, and in practice, often represent the mathematical expectation of a function of interest. In cases using large dimensions, these methods can significantly reduce the calculation time required by deterministic methods. Monte-Carlo methods involve drawing a series of samples, distributed following a target distribution. The main generation methods, including importance sampling, the acceptance-rejection method, the Gibbs sampler, etc., will be presented. Another objective is to minimize the mean square error between the calculated and true values, and variance reduction methods will be studied using simulations.
Second order stationary process
The fourth chapter covers second order random stationary processes in the broadest sense: Wide Sense Stationary (WSS). The chapter is split into three parts, beginning with empirical second order estimators, leading to the correlogram. Then follow general and detailled results on the linear prediction which is fundamental role in the WSS time series. The third part is devoted to the non-parametric spectral estimation approaches (smooth periodograms, average periodograms, etc.). A detailed discussion on the bias-variance compromise is given.
Inferences on HMM
States are directly visible in simple Markov models, and the modeling process depends exclusively on transition probabilities. In hidden-state Markov models (HMM), however, states can only be seen via observed signals which are statistically linked to these states. HMMs are particularly useful as control models, using latent variables of mixtures connected to each observation.
A wide variety of problems may be encountered in relation to inference, for example seeking the sequence most likely to have produced a given series of observations; determining the a posteriori distribution of hidden states; estimating the parameters of a model; etc. Key algorithms include the Baum-Welch algorithm and the Viterbi algorithm, to cite the two best-known examples. HMM have applications in a wide range of domains, such as speech recognition (analysis and synthesis), automatic translation, handwriting analysis, activity identification, DNA analysis, etc.
Selected Topics
The final chapter presents applications which use many of the principles and techniques described in the preceding chapters, without falling into any of the categories defined in these chapters. The first section is devoted to high resolution techniques (MUSIC and ESPRIT algorithms), whilst the second covers classic communication problems (coding, modulation, eye diagrams, etc.). The third section presents the Viterbi algorithm, and the fourth is given over to scalar and vectorial quantification.
Annexes
A certain number of functions are given in simplified form in the appendix. This includes a version of the boxplot function, alongside functions associated with the most common distributions (Student, χ2 and Fischer).
Remarques
The notation used in this book is intended to conform to current usage; in cases where this is not the case, every care has been taken to remove any ambiguity as to the precise meaning of terms. On a number of occasions, we refer to nitnslseries instead of nitnsltime series or nitnslsequences to avoid confusion.
