Wavelet Analysis
Subtitle: The Scalable Structure of Information
By: by Howard L. Resnikoff, Raymond O. Wells
Contributors: Wells, Raymond O.
Publisher: Springer New York
Published: 1998
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 435
ISBN-13: 9781461268307; 9781461205937
Subjects: Electronic data processing; Numerical analysis; Engineering; Fourier analysis; Mathematics
Description: The past decade has witnessed the rapid development of a new mathematical tool, called wavlet analysis, for analyzing complex signals. It has begin to play a serious role in applications ranging from communications to geophysics, and from simulations to image processing. Like Fourier analysis (of which it is a generalization), or musical notation, wavelet analysis provides a method for representing a set of complex phenomena in a simpler, more compact, and thus more efficient manner. This text introduces the ideas and methods of wavelet analysis, relates them to previously known methods in mathematics and engineering, and shows how to apply wavelet analysis to digital signal processing. It begins by describing the multiscale (sometimes called "fractal") nature of information in many aspects of the real world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functions on a space. The discussion then turns from the continuous to the discrete and shows how a properly selected set of wavelets can be used to represent -- and even differentiate -- a wide range of signls efficiently and effectively. The last part of the book presents a wide variety of applications of wavelets to probllems in data compression and telecommunications.
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Table of contents: title: Part I: The Scalable Structure of Information: 1. The New Mathematical Engineering; 2. Good Approximations; 3. Wavelets: A Positional Notation for Functions; title: Part II: Wavelet Theory: 4. Algebra and Geometry of Wavelet Matrices; 5. One-Dimensional Wavelet Systems; 6. Examples of One-Dimensional Wavelet Systems; 7. Higher-Dimensional Wavelet Systems; title: Part III: Wavelet Approximation and Algorithms: 8. The Mallat Algorithm; 9. Wavelet Approximation; 10. Wavelet Calculus and Connection Coefficients; 11. Multiscale Representation of Geometry; 12. Wavelet-Galerkin Solutions of Partial Differential Equations; title: Part IV: Wavelet Applications: 13. Wavelet Data Compression; 14. Modulation and Channel Coding; title: References; title: Index.