Synopses & Reviews
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 thereal world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functins 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.
Synopsis
The authors have been beguiled and entranced by mathematics all of their lives, and both believe it is the highest expression of pure thought and an essential component-one might say the quintessence-of nature. How else can one ex plain the remarkable effectiveness of mathematics in describing and predicting the physical world? The projection of the mathematical method onto the subspace of human endeav 1 ors has long been a source of societal progress and commercial technology. The invention of the electronic digital computer (not the mechanical digital computer of Babbage) has made the role of mathematics in civilization even more central by making mathematics active in the operation of products. The writing of this book was intertwined with the development of a start-up company, Aware, Inc. Aware was founded in 1987 by one of the authors (H.L.R.), and the second author (R.O.W.) put his shoulder to the wheel as a consultant soon after."
Synopsis
This text gives a clear introduction to the ideas and methods of wavelet analysis, making concepts understandable by relating them to methods in mathematics and engineering. It shows how to apply wavelet analysis to digital signal processing and presents a wide variety of applications.
Table of Contents
Part I: The Scalable Structure of Information; 1. The New Mathematical Engineering; 2. Good Approximations; 3. Wavelets: A Positional Notation for Functions; 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; 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 Differentail Equations; Part IV: Wavelet Applications; 13. Wavelet Data Compression; 14. Modulation and Channel Coding; Bibliography