Wavelet Analysis

The Scalable Structure of Information

Howard L. Resnikoff, Raymond O. Wells

452 pages, parution le 01/01/2002

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Résumé

The past decade has witnessed the rapid development of a new mathematical tool, called wavelet 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.

Written for: Applied mathematicans, electrical engineers, computer scientists

Sommaire

The Scalable Structure of Information
- The New Mathematical Engineering
- Good Approximations
- Wavelets: A Positional Notation for Functions
Wavelet Theory
- Algebra and Geometry of Wavelet Matrices
- One-Dimensional Wavelet Systems
- Examples of One-Dimensional Wavelet Systems
- Higher-Dimensional Wavelet Systems
Wavelet Approximation and Algorithms
- The Mallat Algorithm
- Wavelet Approximation
- Wavelet Calculus and Connection Coefficients
- Multiscale Representation of geometry
- Wavelet-Galerkin Solutions of partial Differentail Equations
Wavelet Applications
- Wavelet Data Compression
- Modulation and Channel Coding

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Howard L. Resnikoff, Raymond O. Wells
Parution	01/01/2002
Nb. de pages	452
Format	16 x 24
Couverture	Relié
Poids	780g
Intérieur	Noir et Blanc
EAN13	9780387983837
ISBN13	978-0-387-98383-7