Wavelet Toolware Software for Wavelet Training-[Charles Chui, Andrew Chan, C Steve Liu].pdf

Wavelet Toolware:
Software for Wavelet Training
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Wavelet Toolware:
Software for Wavelet Training
Andrew K. Chan
Department of Electrical Engineering
Texas A&M University
Steve J. Liu
Department puter Science
Texas A&M University
San Diego London Boston
New York Sydney Tokyo Toronto
This book is printed on acid free paper.
Copyright © 1998 by Academic Press
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Disclaimer:
This eBook does not include the ancillary media that was
packaged with the original printed version of the book.
Contents
Part I ii
From Fourier Analysis to Wavelet Analysis 1
Short-Time Fourier Transform 2
Window Measures 3
What Is a Wavelet? 5
Wavelets at different resolutions (scales) 6
Continuous Wavelet Transform 7
Multiresolution Analysis 9
Two-scale relations 12
position relation 13
Development of the position and reconstruc-
tion algorithms 15
Mapping of functions into the approximation space 16
Types of Wavelets 18
Orthonormal wavelet bases 18
Semi-orthogonal wavelet bases 19
Biorthogonal wavelet bases 21
Wavelet Packets 22
Wavelet packet algorithms 23
Two-Dimensional Wavelets 24
Two-dimensional wavelet packets 26
Part II 27
Wavelet Algorithms Overview 29
Algorithm puting the STFT 29
Algorithm puting the CWT 31
a