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1、INGRIDDAUBECHIESRutgersUniversityandAT&TBellLaboratoriesTenLecturesonWaveletsSOCIETYFORINDUSTRIALANDAPPLIEDMATHEMATICSPHILADELPHIA,PENNSYLVANIA1992Copyright1992bytheSocietyforIndustrialandAppliedMathematicsAllrightsreserved.Nopartofthisbookmaybereproduced,stored,ortransmittedinanymanner
2、withoutthewrittenpermissionofthePublisher.Forinformation,writetheSocietyforIndustrialandAppliedMathematics,3600UniversityCityScienceCenter,Philadelphia,Pennsylvania19104-2688.SecondPrinting1992ThirdPrinting1994FourthPrinting1995FifthPrinting1997SixthPrinting1999LibraryofCongressCatalogi
3、ng-in-PublicationDataDaubechies,Ingrid.Tenlecturesonwavelets/IngridDaubechies.p.cm.-(CBMS-NSFregionalconferenceseriesinappliedmathematics;61)Includesbibliographicalreferencesandindex.ISBN0-89871-274-21.Wavelets(Mathematics)-Congresses.I.Title.II.Series.QA403.3.D381992515'.2433-dc2092-13
4、201sianL.isaregisteredtrademark.Tomymother,whogavemethewilltobeindependent.Tomyfather,whostimulatedmyinterestinscience.iiiContentsVllINTRODUCTIONxiPRELIMINARIESANDNOTATIONCHAPTER1:TheWhat,Why,andHowofWavelets17CHAPTER2:TheContinuousWaveletTransfonn53CHAPTER3:DiscreteWaveletTransfonns:Fr
5、ames107CHAPTER4:Time-FrequencyDensityandOrthononnalBases129CHAPTER5:OrthononnalBasesofWaveletsandMultiresolutionAnalysis167CHAPTER6:OrthononnalBasesofCompactlySupportedWavelets215CHAPTER7:MoreAbouttheRegularityofCompactlySupportedWavelets251CHAPTER8:SymmetryforCompactlySupportedWaveletB
6、ases289CHAPTER9:CharacterizationofFunctionalSpacesbyMeansofWavelets313CHAPTER10:GeneralizationsandTricksforOrthononnalWaveletBases341REFERENCES353SUBJECTINDEX355AUTHORINDEXvIntroductionWaveletsarearelativelyrecentdevelopmentinappliedmathematics.Theirnameitselfwascoinedapproximatelyadeca
7、deago(Morlet,Arens,Fourgeau,andGiard(1982),Morlet(1983),GrossmannandMorlet(1984));inthelasttenyearsinterestinthemhasgrownatanexplosiverate.Thereareseveralreasonsfortheirpresentsuccess.Ontheonehand,theconceptofwaveletscanbeviewedasasynthesisofideaswhichoriginatedduringthelasttwe
