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  • Textbook
  • © 1998

Wavelet Analysis

The Scalable Structure of Information

  • Wavelet analysis plays a serious role in applications ranging from communications to geophysics, and from simulations to image processing
  • This book gives a clear introduction to the ideas and methods of wavelet analysis
  • It makes concepts understandable by relating them to previously known methods in mathematics and engineering
  • Shows how to apply wavelet analysis to digital signal processing
  • Presents a wide variety of applications of wavelets to problems in data compression and telecommunications

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvi
  2. The Scalable Structure of Information

    1. Front Matter

      Pages 1-1
    2. The New Mathematical Engineering

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 3-11
    3. Good Approximations

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 12-29
    4. Wavelets: A Positional Notation for Functions

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 30-36
  3. Wavelet Theory

    1. Front Matter

      Pages 37-37
    2. Algebra and Geometry of Wavelet Matrices

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 39-85
    3. One-Dimensional Wavelet Systems

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 86-139
    4. Examples of One-Dimensional Wavelet Systems

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 140-164
    5. Higher-Dimensional Wavelet Systems

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 165-187
  4. Wavelet Approximation and Algorithms

    1. Front Matter

      Pages 189-189
    2. The Mallat Algorithm

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 191-201
    3. Wavelet Approximation

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 202-235
    4. Wavelet Calculus and Connection Coefficients

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 236-265
    5. Multiscale Representation of Geometry

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 266-279
    6. Wavelet—Galerkin Solutions of Partial Differential Equations

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 280-340
  5. Wavelet Applications

    1. Front Matter

      Pages 341-341
    2. Wavelet Data Compression

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 343-365
    3. Modulation and Channel Coding

      • Howard L. Resnikoff, Raymond O. Wells Jr.
      Pages 366-396
  6. Back Matter

    Pages 397-435

About this book

The authors have been beguiled and entranced by mathematics all of their lives, and both believe it is the highest expression of pure thought and an essential component-one might say the quintessence-of nature. How else can one ex­ plain the remarkable effectiveness of mathematics in describing and predicting the physical world? The projection of the mathematical method onto the subspace of human endeav­ 1 ors has long been a source of societal progress and commercial technology. The invention of the electronic digital computer (not the mechanical digital computer of Babbage) has made the role of mathematics in civilization even more central by making mathematics active in the operation of products. The writing of this book was intertwined with the development of a start-up company, Aware, Inc. Aware was founded in 1987 by one of the authors (H.L.R.), and the second author (R.O.W.) put his shoulder to the wheel as a consultant soon after.

Authors and Affiliations

  • Future WAVE Inc., Boston, USA

    Howard L. Resnikoff

  • Department of Mathematics, Rice University, Houston, USA

    Raymond O. Wells

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access