Overview

Wavelets allow complex information such as music, speech, images and patterns to be decomposed into elementary forms - called the fundamental building blocks at different positions and scales - and subsequently reconstructed with high precision. With an increased demand for mathematical tools to provide both theory and applications for science and engineering, the utility and interest of wavelet analysis intense and pervasive in all disciplines. Wavelet Transforms and Their Applications presents both a systematic exposition of the basic ideas and results of wavelet transforms and their applications in time-frequency signal analysis and turbulence. Throughout the book the major emphasis is on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. The book provides a large number of examples, which are either directly associated with applications or formulated in terms of the mathematical, physical and engineering context in which the theory arises. While other textbooks aim to a mathematically matured audience, this book is an introduction to wavelet transforms and accessible to a larger audience with diverse background and interests in mathematics, science and engineering.

Full Product Details

Author:   Lokenath Debnath
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   2002 ed.
Dimensions:   Width: 15.60cm , Height: 3.10cm , Length: 23.40cm
Weight:   0.995kg
ISBN:  

9780817642044

ISBN 10:   0817642048
Pages:   565
Publication Date:   16 November 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Replaced By:   9780817684174
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

Preface Brief Historical Introduction Hilbert Spaces and Orthonormal Systems Fourier Transforms and Their Applications The Gabor Transform and Time-Frequency Signal Analysis The Wigner-Ville Distribution and Time-Frequency Signal Analysis Wavelet Transforms and Basic Properties Multiresolution Analysis and Construction of Wavelets Newland's Harmonic Wavelets Wavelet Transform Analysis of Turbulence Answers and Hints for Selected Exercises Bibliography Index

Reviews

It contains a wealth of information that should make it useful in signal processing and perhaps some other areas of engineering ... I like the book as a possible text for a beginning graduate course in, say, mathematical methods in engineering. It covers a number of topics that are quite useful but are rarely covered in mainstream mathematics courses ... a lot of the proofs are short and computational, which is necessary in such a book that covers a large number of topics ... it would serve as a good text, provided that the aim of the course is to present a variety of transforms useful in signal processing, as well as the wavelet transforms. --Mathematical Reviews The last two decades have produced tremendous developments in the mathematical theory of wavelets and their great variety of applications. Since wavelet analysis is a relatively new subject, this monograph is intended to be self-contained. The book is designed as a modern and authoritative guide to wavelets, wavelet transform, time-frequency signal analysis and related topics. It is known that some research workers look upon wavelets as a new basis for representing functions, others consider them as a technique for time-frequency analysis and some others think of them as a new mathematical subject. All these approaches are gathered in this book, which presents an accessible, introductory survey of new wavelet analysis tools and the way they can be applied to fundamental analysis problems. We point out the clear, intuitive style of [the] presentation, and the numerous examples demonstrated through[out] the book illustrate how methods work in a step-by-step manner. This way, the book becomes ideal for a broad audience including advanced undergraduate students, graduate[s] and professionals in signal processing. Also, the book provides the reader with a thorough mathematical background, and the wide variety of applications cover the interdisciplinary collaborative research in applied mathematics. --Revue D'Analyse Numerique et de Theorie de L'Approximation

It contains a wealth of information that should make it useful in signal processing and perhaps some other areas of engineering . . . I like the book as a possible text for a beginning graduate course in, say, mathematical methods in engineering. It covers a number of topics that are quite useful but are rarely covered in mainstream mathematics courses . . . a lot of the proofs are short and computational, which is necessary in such a book that covers a large number of topics . . . it would serve as a good text, provided that the aim of the course is to present a variety of transforms useful in signal processing, as well as the wavelet transforms. <p>a Mathematical Reviews <p> The last two decades have produced tremendous developments in the mathematical theory of wavelets and their great variety of applications. Since wavelet analysis is a relatively new subject, this monograph is intended to be self-contained. The book is designed as a modern and authoritative guide to wavelets, wavelet transform, time-frequency signal analysis and related topics. <p>It is known that some research workers look upon wavelets as a new basis for representing functions, others consider them as a technique for time-frequency analysis and some others think of them as a new mathematical subject. All these approaches are gathered in this book, which presents an accessible, introductory survey of new wavelet analysis tools and the way they can be applied to fundamental analysis problems. We point out the clear, intuitive style of [the] presentation, and the numerous examples demonstrated through[out] the book illustrate how methods work in a step-by-step manner. <p>This way, the book becomesideal for a broad audience including advanced undergraduate students, graduate[s] and professionals in signal processing. Also, the book provides the reader with a thorough mathematical background, and the wide variety of applications cover the interdisciplinary collaborative research in applied mathematics. <p>a Revue Da (TM)Analyse NumA(c)rique et de ThA(c)orie de La (TM)Approximation

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