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An Introduction to Wavelet Analysis

  • David F. Walnut

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. David F. Walnut
      Pages 3-25
    3. David F. Walnut
      Pages 27-57
    4. David F. Walnut
      Pages 59-86
    5. David F. Walnut
      Pages 87-111
  3. The Haar System

    1. Front Matter
      Pages 113-113
    2. David F. Walnut
      Pages 115-140
    3. David F. Walnut
      Pages 141-159
  4. Orthonormal Wavelet Bases

    1. Front Matter
      Pages 161-161
    2. David F. Walnut
      Pages 163-214
    3. David F. Walnut
      Pages 215-248
    4. David F. Walnut
      Pages 249-285
  5. Other Wavelet Constructions

    1. Front Matter
      Pages 287-287
    2. David F. Walnut
      Pages 289-333
    3. David F. Walnut
      Pages 335-368
  6. Applications

    1. Front Matter
      Pages 369-369
    2. David F. Walnut
      Pages 371-395
    3. David F. Walnut
      Pages 397-421
  7. Back Matter
    Pages 423-451

About this book

Introduction

An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. All readers will find

Keywords

Fourier analysis Fourier transform Functional Analysis Hilbert space MATLAB Mathematics algebra wavelets

Authors and affiliations

  • David F. Walnut
    • 1
  1. 1.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0001-7
  • Copyright Information Birkhäuser Boston 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6567-2
  • Online ISBN 978-1-4612-0001-7
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site