Wavelets Made Easy

1. Front Matter

   Pages i-xi

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2. Algorithms for Wavelet Transforms

   1. Front Matter

      Pages 1-1

      PDF

   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

      PDF

   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

      PDF

   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

   PDF

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.

• 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

"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

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

  Yves Nievergelt

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