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Wavelets Made Easy

  • Yves Nievergelt

Table of contents

  1. Front Matter
    Pages i-xi
  2. Algorithms for Wavelet Transforms

    1. Front Matter
      Pages 1-1
    2. Yves Nievergelt
      Pages 3-35
    3. Yves Nievergelt
      Pages 36-72
    4. Yves Nievergelt
      Pages 73-113
  3. Basic Fourier Analysis

    1. Front Matter
      Pages 115-115
    2. Yves Nievergelt
      Pages 117-146
    3. Yves Nievergelt
      Pages 147-174
    4. Yves Nievergelt
      Pages 175-201
  4. Computation and Design of Wavelets

    1. Front Matter
      Pages 203-203
    2. Yves Nievergelt
      Pages 205-237
    3. Yves Nievergelt
      Pages 238-261
    4. Yves Nievergelt
      Pages 262-283
  5. Back Matter
    Pages 285-297

About this book

Introduction

This book, written at the level of a first course in calculus and linear algebra, offers a lucid and concise explanation of mathematical wavelets. Evolving from ten years of classroom use, its accessible presentation is designed for undergraduates in a variety of disciplines (computer science, engineering, mathematics, mathematical sciences) as well as for practising professionals in these areas.

This unique text starts the first chapter with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra.

The second part of this book provides the foundations of least squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets.

Numerous exercises, a bibliography, and a comprehensive index
combine to make this book an excellent text for the classroom as well as a valuable resource for self-study.

Keywords

Applications of Mathematics Numerical Mathematics Wavelets ksa approximation computer convolution data compression discrete Fourier transform (DFT) fast Fourier transform (FFT) fourier analysis Fourier transform Haar wavelet Interpolation material numerical analysis signal wavelet wavelet transform

Authors and affiliations

  • Yves Nievergelt
    • 1
  1. 1.Department of MathematicsEastern Washington UniversityCheneyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0573-9
  • Copyright Information Springer Science+Business Media New York 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6823-9
  • Online ISBN 978-1-4612-0573-9
  • Buy this book on publisher's site
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