AFriendlyGuidetoWavelets

小波变换入门文档To Yadwiga-Wanda and stanistaw wtodekto Teofila and Franciszek Kowalikand to their children Janusz, Krystym, Mirek, and reniaRisking their collective lives, they took a strangers'infantinto their homes and hearts. Who among us would havethe heart and the courage of these simple country peopleTo my mother Cesia, who survived the Nazi horrors,and to my father Bernard, who did notand to the uncounted multitude of others, less fortunate than Iwho did not live to sing their songA Friendly guideto WaveletsGerald KaiserReprint of the 1994 EditionE BirkhauserGerald KaiserCenter for Signals and waves3608 Govalle avenueAustin, tX78702U.S.Akaiser wavelets. comwww.waveletscomOriginally published as a hard cover editionISBN978-0-8176-81104e-ISBN978-0-8176-8111-1DOI10.1007978-0-8176-8111-1Mathematics Subject Classification(2010): 15-XX, 30-XX, 31-XX, 32-XX, 35-XX, 41-XX,42-XX,44XX,46XX,65-X,78xX,94XXC Gerald Kaiser 2011All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer Science +Business Media, LLC, 233 Spring Street, New York, NY10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connectionwith any form of information storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed is forbiddenThe use in this publication of trade names, trademarks, service marks, and similar terms, even if they arenot identified as such, is not to be taken as an expression of opinion as to whether or not they are subjecto proprietary rightsPrinted on acid-free paperbirkhauser-science. come BirkhauserGERALD KAISERa Friendly guideto WaveletsBirkhauserBoston· Basel· Berlin1994Gerald KaiserThe Virginia Center for Signals and Waves1921 Kings RoadGlen Allen. vA 23060Library of Congress Cataloging-in-Publication DataKaiser. Geralda friendly guide to wavelets/ gerald KaiserpIncludes bibliographical references and indexISBN 0-8176-3711-7(acid-free).--IsBN 3-7643-3711-7(acid-free)1. Wavelets. I. TitleQA403.3.K35199494-29118515.2433-dc20CIPPrinted on acid-free paperBirkhauser◎ Gerald Kaiser1994Sixth printing, 1999All rights reserved This work may not be translated or copied in whole or in part withoutthe written permission of the publisher(Birkhauser Boston, c/o Springer-Verlag NewYork, Inc, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts inconnection with reviews or scholarly analysis use in connection with any form ofinformation storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed is forbidden.The use of general descriptive names, trade names, trademarks, etc. in this publication,even if the former are not especially identified is not to be taken as a sign that such namesas understood by the Trade marks and Merchandise Marks Act, may accordingly be usedfreely by anyoneISBN0-8176-3711-7ISBN3-7643-3711-7Typeset by Martin Stock, Cambridge, MAPrinted and bound by quinn-Woodbine, Woodbine NJPrinted in the u.s.a9876ContentsPrefaceSuggestions to the Reader....,.·ⅹVSymbols, Conventions, and Transforms,Ⅹ1XPart I: Basic Wavelet Analysis1. Preliminaries: Background and Notation1.1 Linear Algebra and Dual Bases1.2 Inner Products, Star Notation, and Reciprocal Bases..... 121.3 Function Spaces and Hilbert Spaces.............191.4 Fourier Series, Fourier Integrals, and Signal Processing.... 261.5 Appendix: Measures and Integrals34Exercises,412. Windowed fourier transforms2.1 Motivation and Definition of the Wft442.2 Time-Frequency Localization502. 3 The Reconstruction Formula532.4 Signal Processing in the Time-Frequency Domain......56Exercises3. Continuous wavelet Transforms3. 1 Motivation and Definition of the Wavelet Transform ..... 603.2 The reconstruction formula.643.3 Frequency Localization and Analytic Signals703.4 Wavelets, Probability Distributions, and Detail....... 73Exercises77A Friendly guide to Wavelets4. Generalized Frames: Key to Analysis and Synthesis4. 1 From Resolutions of Unity to Frames .......,................784.2 Reconstruction Formula and Consistency Condition..854.3 Discussion: Frames versus bases .............................884. 4 Recursive reconstruction894.5 Discrete Frames···.···········914.6 Roots of Unity: A Finite-Dimensional ExampleExercises········,······965. Discrete Time-Frequency Analysis and Sampling5. 1 The Shannon Sampling Theorem ............................995.2 Sampling in the Time-Frequency Domain.......... 1025.3 Time Sampling versus Time-Frequency Sampling...,...1105.4 Other Discrete Time-Frequency Subframes...1125.5 The Question of OrthogonalityExercises .................................................1216. Discrete Time-Scale Analysis6.1 Sampling in the Time-Scale domain1236.2 Discrete Frames with Band-Limited Wavelets ...............1246.3 Other Discrete Wavelet frames.133Exercises1377. Multiresolution Analysis7.1 The idea···.:·●··.,1397.2 Operational Calculus for Subband Filtering Schemes .... 1477. 3 The View in the Frequency domain.,,,1607.4 Frequency Inversion Symmetry and Complex Structure ... 1697.5 Wavelet Packets····.···甲····Exercises1748. Daubechies' Orthonormal Wavelet Bases8.1 Construction of FIR Filters..1768.2 Recursive Construction of in the Frequency Domain ... 1833. 3 Recursion in Time: Diadic Interpolation.189Contents8. 4 The method of Cumulants酯自1918.5 Plots of daubechies wavelets..197Exercises...,.197Part II: Physical Wavelets9. Introduction to Wavelet Electromagnetics9.1 Signals and Waves....,................. 2039.2 Fourier Electromagnetics,2069. 3 The Analytic-Signal Transform∴..2159. 4 Electromagnetic Wavelets2249.5 Computing the Wavelets and Reproducing Kernel9.6 Atomic Composition of Electromagnetic Waves ....... 2339.7 Interpretation of the Wavelet Parameters .......... 2369. 8 Conclusions······鲁··24410. Applications to Radar and Scattering10. 1 Ambiguity Functions for Time Signals10.2 The Scattering of Electromagnetic Wavelets25611. Wavelet Acoustics11.1 Construction of Acoustic Wavelets.27111.2 Emission and absorption of Wavelets.......,.... 27511.3 Nonunitarity and the rest frame of the Medium...... 28111.4 Examples of Acoustic Wavelets ............... 283References,,,291Index番·D酯鲁鲁4音鲁··垂297