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  • Textbook
  • © 2015

Wavelet Transforms and Their Applications

Birkhäuser
  • Includes exercises at the end of each chapter and provides a section of selected answers to exercises

  • Differs from many textbooks due to major emphasis placed on numerous topics and systematic development of underlying theories

  • Provides an introduction to wavelet transforms while being accessible to a broad audience

  • New revised chapters on Extensions of Multiresolution Analysis, New Lawds’s Harmonic Wavelets, and Applications of Wavelet Transforms

  • Includes supplementary material: sn.pub/extras

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-0-8176-8418-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 109.99
Price excludes VAT (USA)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
  2. Brief Historical Introduction

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 1-27
  3. Hilbert Spaces and Orthonormal Systems

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 29-127
  4. Fourier Transforms and Their Applications

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 129-242
  5. The Gabor Transform and Time–Frequency Signal Analysis

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 243-286
  6. The Wigner–Ville Distribution and Time–Frequency Signal Analysis

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 287-336
  7. The Wavelet Transforms and Their Basic Properties

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 337-373
  8. Multiresolution Analysis and Construction of Wavelets

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 375-440
  9. Extensions of Multiresolution Analysis

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 441-473
  10. Newland’s Harmonic Wavelets

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 475-487
  11. Wavelet Transform Analysis of Turbulence

    • Lokenath Debnath, Firdous Ahmad Shah
    Pages 489-516
  12. Back Matter

    Pages 517-553

About this book

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.

Numerous standard and challenging topics, applications, and exercises are included in this edition, which will stimulate research interest among senior undergraduate and graduate students. The book contains 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 wavelet theory arises.

Topics and Features of the Second Edition:

·         Expanded and revised the historical introduction by including many new topics such as the fractional Fourier transform, and the construction of wavelet bases in various spaces other than  and several new extensions of the original multiresolution analysis.

·         Extensions of the classical theory of multiresolution analysis consisting of Ƥ-multiresolution analysis on the positive half-line  and non-uniform multiresolution analysis.

·         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

·         Completely updated bibliography and enlarged index

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.

Keywords

  • Fourier Transforms
  • Harmonic Wavelets
  • Multiresolution Analysis
  • Time-Frequency Analsysis
  • Wavelets

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)

Authors and Affiliations

  • Department of Mathematics, University of Texas, Pan American, Edinburg, USA

    Lokenath Debnath

  • Department of Mathematics, University of Kashmir, Anantnag, India

    Firdous Ahmad Shah

About the authors

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.

Bibliographic Information

  • Book Title: Wavelet Transforms and Their Applications

  • Authors: Lokenath Debnath, Firdous Ahmad Shah

  • DOI: https://doi.org/10.1007/978-0-8176-8418-1

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Science+Business Media New York 2015

  • Hardcover ISBN: 978-0-8176-8417-4

  • eBook ISBN: 978-0-8176-8418-1

  • Edition Number: 2

  • Number of Pages: XV, 553

  • Number of Illustrations: 60 b/w illustrations

  • Topics: Signal, Speech and Image Processing , Functional Analysis, Applications of Mathematics

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-0-8176-8418-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 109.99
Price excludes VAT (USA)