Wavelets and Multiscale Signal Processing  book cover
1st Edition

Wavelets and Multiscale Signal Processing

ISBN 9781315898582
Published June 30, 2020 by Chapman and Hall/CRC
248 Pages

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Book Description

Since their appearance in mid-1980s, wavelets and, more generally, multiscale methods have become powerful tools in mathematical analysis and in applications to numerical analysis and signal processing. This book is based on "Ondelettes et Traitement Numerique du Signal" by Albert Cohen. It has been translated from French by Robert D. Ryan and extensively updated by both Cohen and Ryan. It studies the existing relations between filter banks and wavelet decompositions and shows how these relations can be exploited in the context of digital signal processing. Throughout, the book concentrates on the fundamentals. It begins with a chapter on the concept of multiresolution analysis, which contains complete proofs of the basic results. The description of filter banks that are related to wavelet bases is elaborated in both the orthogonal case (Chapter 2), and in the biorthogonal case (Chapter 4). The regularity of wavelets, how this is related to the properties of the filters and the importance of regularity for the algorithms are the subjects of Chapter 3. Chapter 5 looks at multiscale decomposition as it applies to stochastic processing, in particular to signal and image processing.

Table of Contents

1. Multiresolution Analysis. Introduction 2. Wavelets and Conjugate Quadrature Filters 3. The Regularity of Scaling Functions and Wavelets 4. Biorthogonal Wavelet Bases 5. Stochastic Processes. A Quasi-Analytic Wavelet Bases. B Multivariate Constructions. C Multiscale Unconditional Bases. D Notation.

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Albert Cohen