A Primer on Wavelets and Their Scientific Applications / Edition 1

A Primer on Wavelets and Their Scientific Applications / Edition 1

by James S. Walker, Steven G. Krantz
     
 

The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a

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Overview

The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques.

Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.

Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.

Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.

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Product Details

ISBN-13:
9780849382765
Publisher:
Taylor & Francis
Publication date:
03/26/1999
Series:
Studies in Advanced Mathematics Series
Edition description:
Older Edition
Pages:
168
Product dimensions:
6.00(w) x 9.00(h) x 0.60(d)

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Table of Contents

1Haar Wavelets1
1.1The Haar transform1
1.2Conservation and compaction of energy6
1.3Haar wavelets10
1.4Multiresolution analysis13
1.5Compression of audio signals18
1.6Removing noise from audio signals23
1.7Notes and references28
2Daubechies wavelets29
2.1The Daub4 wavelets29
2.2Conservation and compaction of energy38
2.3Other Daubechies wavelets42
2.4Compression of audio signals49
2.5Quantization, entropy, and compression53
2.6Denoising audio signals58
2.7Two-dimensional wavelet transforms65
2.8Compression of images72
2.9Fingerprint compression75
2.10Denoising images79
2.11Some topics in image processing87
2.12Notes and references92
3Frequency analysis95
3.1Discrete Fourier analysis95
3.2Definition of the DFT and its properties98
3.3Frequency description of wavelet analysis103
3.4Correlation and feature detection108
3.5Object detection in 2D images114
3.6Creating scaling signals and wavelets118
3.7Notes and references122
4Beyond wavelets123
4.1Wavelet packet transforms123
4.2Applications of wavelet packet transforms126
4.3Continuous wavelet transforms129
4.4Gabor wavelets and speech analysis134
4.5Notes and references138
ASoftware for wavelet analysis139
References145
Index151

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