Matlab - Wavelet Toolbox - User's Guide - Version 2.pdf

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Wavelet
Wavelet
For Use with M ATLAB ®
Michel Misiti
Yves Misiti
Georges Oppenheim
Jean-Michel Poggi
Compu tation
Visuali zation
Program ming
User’s Guide
Version 2
Toolbox
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For contact information about worldwide offices, see the MathWorks Web site.
Wavelet Toolbox User’s Guide
COPYRIGHT 1997 - 2002 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or repro-
duced in any form without prior written consent from The MathWorks, Inc .
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by
or for the federal government of the United States. By accepting delivery of the Program, the government
hereby agrees that this software qualifies as "commercial" computer software within the meaning of FAR
Part 12.212, DFARS Part 227.7202-1, DFARS Part 227.7202-3, DFARS Part 252.227-7013, and DFARS Part
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Target Box is a trademark of The MathWorks, Inc.
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Printing History: March 1997
First printing
New for Version 1
September 2000 Second printing Revised (Release 12)
June 2001
Online only
Revised (Release 12)
July 2002
Online only
Revised (Release 13) Version 2.2
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Contents
Preface
About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Notes by Yves Meyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
Notes by Ingrid Daubechies . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
What Is the Wavelet Toolbox? . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
Using This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
New Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Experienced Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
All Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Caution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii
For More Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii
Installing the Wavelet Toolbox . . . . . . . . . . . . . . . . . . . . . . . . xxiv
System Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv
Platform-Specific Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv
Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . xxvi
Related Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii
i
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1
Wavelets: A New Tool for Signal Analysis
Wavelet Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Scale Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Time Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Wavelet Decomposition as a Whole . . . . . . . . . . . . . . . . . . . . . . . 1-4
Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Short-Time Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
What Can Wavelet Analysis Do? . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
What Is Wavelet Analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9
Number of Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9
The Continuous Wavelet Transform . . . . . . . . . . . . . . . . . . . 1-10
Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11
Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Five Easy Steps to a Continuous Wavelet Transform . . . . . . . 1-12
Scale and Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
The Scale of Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
What’s Continuous About the Continuous Wavelet
Transform? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-17
The Discrete Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . 1-18
One-Stage Filtering: Approximations and Details . . . . . . . . . . 1-18
Multiple-Level Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
Wavelet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22
Reconstruction Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23
Reconstructing Approximations and Details . . . . . . . . . . . . . . 1-23
Relationship of Filters to Wavelet Shapes . . . . . . . . . . . . . . . . 1-25
Multistep Decomposition and Reconstruction . . . . . . . . . . . . . 1-28
Wavelet Packet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-29
History of Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
ii
Contents
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An Introduction to the Wavelet Families . . . . . . . . . . . . . . . 1-32
Haar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-33
Daubechies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-33
Biorthogonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-34
Coiflets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-35
Symlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-35
Morlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36
Mexican Hat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36
Meyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37
Other Real Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37
Complex Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37
2
Using Wavelets
One-Dimensional Continuous Wavelet Analysis . . . . . . . . . . 2-4
Continuous Analysis Using the Command Line . . . . . . . . . . . . 2-5
Continuous Analysis Using the Graphical Interface . . . . . . . . . 2-8
Importing and Exporting Information from the
Graphical Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17
One-Dimensional Complex Continuous Wavelet Analysis 2-19
Complex Continuous Analysis Using the Command Line . . . . 2-20
Complex Continuous Analysis Using the Graphical Interface 2-22
Importing and Exporting Information from the Graphical
Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
One-Dimensional Discrete Wavelet Analysis . . . . . . . . . . . . 2-28
One-Dimensional Analysis Using the Command Line . . . . . . 2-30
One-Dimensional Analysis Using the Graphical Interface . . . 2-39
Importing and Exporting Information from the Graphical
Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-57
iii
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