Wavelet Transforms and Their Applications

by Lokenath Debnath, Firdous Ahmad Shah

Overview

This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed 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. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.

Product Details

ISBN-13:	9780817684174
Publisher:	Birkhäuser Boston
Publication date:	11/25/2014
Edition description:	2nd ed. 2015
Pages:	553
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

About the Author

Lokenath Debnath, Ph.D., is a Professor of Mathematics at The University of Texas-Pan American. He received his Ph.D. in Applied Mathematics from the University of London, and a Ph.D. in Pure Mathematics from the University of Calcutta. His areas of interest are applied mathematics, applied partial differential equations, integral transforms, fluid dynamics, and continuum mechanics. Firdous Ahmad Shah, Ph.D., is an Assistant Professor in the Post Graduate Department of Mathematics at the University of Kashmir. His areas of specialization are: wavelets, wavelet packets, applications of wavelets in financial time series, and wavelet neural networks.

Table of Contents

Brief Historical Introduction.- Hilbert Spaces and Orthonormal Systems.- Fourier Transformations and Their Applictions.- The Gabor Transform and Time-Frequency Signal Analysis.- The Wigner-Ville Distribution and Time-Frequency Signal Analysis.- The Wavelet Transforms and Their Basic Properties.- Multiresolution Analysis and Construction of Wavelets.- Extensions of Multiresolution Analysis.- Newland's Harmonic Wavelets.- Wavelet Transform Analysis of Turbulence.

Editorial Reviews

It can be seen as a reference text or as a study book, complete with definitions, theorems, proofs and exercises. … The book is an up to date reference work on univariate Fourier and wavelet analysis including recent developments in multiresolution, wavelet analysis, and applications in turbulence. The systematic construction of the chapters with extensive lists of exercises make it also very suitable for teaching.” (Adhemar Bultheel, euro-math-soc.eu, February, 2015)

“The book is primarily aimed at advanced undergraduates and graduate students across all of applied mathematics. It is a good source of information for all professionals interested in wavelet transforms and their applications.” (Yuri A. Farkov, zbMATH 1308.42030, 2015)

From the Publisher