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Birkhäuser

Wavelets Made Easy

  • Textbook
  • © 1999

Overview

Authors:
  1. Yves Nievergelt

    1. Department of Mathematics, Eastern Washington University, Cheney, USA

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xi
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  2. Algorithms for Wavelet Transforms

    1. Front Matter

      Pages 1-1
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    2. Haar’s Simple Wavelets

      • Yves Nievergelt
      Pages 3-35

    3. Multidimensional Wavelets and Applications

      • Yves Nievergelt
      Pages 36-72

    4. Algorithms for Daubechies Wavelets

      • Yves Nievergelt
      Pages 73-113

  3. Basic Fourier Analysis

    1. Front Matter

      Pages 115-115
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    2. Inner Products and Orthogonal Projections

      • Yves Nievergelt
      Pages 117-146

    3. Discrete and Fast Fourier Transforms

      • Yves Nievergelt
      Pages 147-174

    4. Fourier Series for Periodic Functions

      • Yves Nievergelt
      Pages 175-201

  4. Computation and Design of Wavelets

    1. Front Matter

      Pages 203-203
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    2. Fourier Transforms on the Line and in Space

      • Yves Nievergelt
      Pages 205-237

    3. Daubechies Wavelets Design

      • Yves Nievergelt
      Pages 238-261

    4. Signal Representations with Wavelets

      • Yves Nievergelt
      Pages 262-283

  5. Back Matter

    Pages 285-297
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Keywords

About this book

This book explains the nature and computation of mathematical wavelets, which provide a framework and methods for the analysis and the synthesis of signals, images, and other arrays of data. The material presented here addresses the au­ dience of engineers, financiers, scientists, and students looking for explanations of wavelets at the undergraduate level. It requires only a working knowledge or memories of a first course in linear algebra and calculus. The first part of the book answers the following two questions: What are wavelets? Wavelets extend Fourier analysis. How are wavelets computed? Fast transforms compute them. To show the practical significance of wavelets, the book also provides transitions into several applications: analysis (detection of crashes, edges, or other events), compression (reduction of storage), smoothing (attenuation of noise), and syn­ thesis (reconstruction after compression or other modification). Such applications include one-dimensional signals (sounds or other time-series), two-dimensional arrays (pictures or maps), and three-dimensional data (spatial diffusion). The ap­ plications demonstrated here do not constitute recipes for real implementations, but aim only at clarifying and strengthening the understanding of the mathematics of wavelets.

Reviews

"The book explains in a nice way the nature and computation of mathematical wavelets, which provide a framework and methods for the analysis and synthesis of signals, images, and other arrays of data. A useful text for engineers, financiers, scientists, and students looking for explanation of wavelets."

—Journal of Information and Optimization Sciences

"Giving practice first and theory later, the author avoids discouraging readers whose main subject is not mathematics. The book is written in a very comprehensible and lively style. The text is essentially self-contained since many of the facts employed from analysis, linear algebra and functional analysis are stated and partially proved in the book."

—ZAA

Authors and Affiliations

  • Department of Mathematics, Eastern Washington University, Cheney, USA

    Yves Nievergelt

Bibliographic Information

  • Book Title: Wavelets Made Easy

  • Authors: Yves Nievergelt

  • DOI: https://doi.org/10.1007/978-1-4612-0573-9

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-8176-4061-3Published: 28 April 1999

  • Softcover ISBN: 978-1-4612-6823-9Published: 26 February 2014

  • eBook ISBN: 978-1-4612-0573-9Published: 27 November 2013

  • Edition Number: 1

  • Number of Pages: XI, 297

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Applications of Mathematics, Functional Analysis, Electrical Engineering

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