Adapted Wavelet Analysis

This book addresses the properties of wavelet and related transforms, to establish criteria by which the proper analysis tool may be chosen, and details software implementations to perform the needed computation. It is useful for the pure mathematician who is familiar with parts of wavelet theory.

This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients

Autorentext

Mladen Victor Wickerhauser is professor of mathematics and statistics at Washington University, St. Louis. He holds a PhD from Yale University. Professor Wickerhauser's research interests include harmonic analysis, wavelets, and numerical algorithms for data compression. He has six US patents and 118 publications, one of which led to an algorithm used by the FBI to encode fingerprint images.

Inhalt

1. Mathematical Preliminaries 2. Programming Techniques 3. The Discrete Fourier Transform 4. Local Trigonometric Transforms 5. Quadrature Filters 6. The Discrete Wavelet Transform 7. Wavelet Packets 8. The Best Basis Algorithm 9. Multidimensional Library Trees 10. Time-Frequency Analysis 11. Some Applications