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   -> Volume 5, Issue 8

Book: A first course on wavelets
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Guido Weiss (

PostPosted: Mon Sep 09, 1996 5:51 pm    
Subject: Book: A first course on wavelets
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#1 Book: A first course on wavelets

A First Course on Wavelets

Eugenio Hernandez and Guido Weiss

A Volume in the Studies in Advanced Mathematics Series
Series edited by Steven G Krantz


Wavelet theory had its origin in quantum field theory, signal
analysis, and function space theory. In these areas wavelet-like
algorithms replace the classical Fourier- typeexpansion of a function.
This unique new book is an excellent introduction to the basic
properties of wavelets, from background math to powerful applications.
The authors provide elementary methods for constructing wavelets, and
illustrate several new classes of wavelets.

The text begins with a description of local sine and cosine bases that
have been shown to be very effective in applications. Very little
mathematical background is needed to follow this material. A complete
treatment of band-limited wavelets follows. These are characterized
by some elementary equations, allowing the authors to introduce many
new wavelets. Next, the idea of multiresolution analysis (MRA) is
developed, and the authors includ simplified presentations of previous
studies, particularly for compactly supported wavelets.

The authors also present the basic philosophy that all orthonormal
wavelets are completely characterized by two simple equations, and
that most properties and constructions of wavelets can be developed
using these two equations. Material related to applications is
provided, and constructions of splines wavelets are presented.

Mathematics, engineers, physicists, and anyone with a mathematical
background will find this to be an important text for furthering their
studies on wavelets.


- Several bases generatede by a single function via translations and
- Multiresolution analysis, compactly supported wavelets, and spline
- Band-limited wavelets
- Unconditionality of wavelet bases
- Characterizations of many of the principal objects in the theory of
wavelets, such as low-pass filters and scaling functions


- Presents several classes of new wavelets
- Subjects that are needed for applications are treated very directly
- Includes many graphic displays of constructed wavelets
- Contains applications to harmonic analysis and other branches of

ISBN: 0-8493-8274-2, 512 pp, $64.95

CRC Press, Inc: 1-800-272-7737
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