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
A detail-oriented text that begins with an overview of mathematical prerequisites, followed by chapters that examine the properties of waveforms used in adapted wavelet analysis: discrete "fast" Fourier transforms, orthogonal and biorthogonal wavelets, wavelet packets, and localized trigonometric or lapped orthogonal functions. 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 source code (on optional diskette) and closes with a list of worked exercises. Annotation copyright Book News, Inc. Portland, Or.
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.
