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Adapted Wavelet Analysis From Theory to Software

Langue : Anglais

Auteur :

Couverture de l’ouvrage Adapted Wavelet Analysis
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
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
Academic and Professional Practice & Development

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.

This book offers comprehensive detailed coverage of waveforms used in adapted wavelet analysis. Each chapter addresses technical aspects of implementation, provides examples in pseudocode, and includes a list of worked exercises. Begining with an overview of mathematical prerequisites, successive chapters rigorously examine the properties of waveforms used in adapted wavelet analysis. Other chapters discuss the 'best-basis' method, time-frequency analysis and combinations of these algorithms useful for signal analysis, denoising, and data compression. Each chapter discusses the technical aspects of implementation, giving examples in pseudocode backed up with a standard C course code, and closes with a list of worked exercises.