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.

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9780817684174

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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

Author Information

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.

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