框架及其在信號處理中的應用.pdf

1、陜西師范大學碩士學位論文框架及其在信號處理中的應用姓名：郭曉旋申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：李萬社20070501AbslractFrameandapplicationinsignalprocessingGuoXiaoxuanAbstractWaveletanalysismademilestonelikeprogressintheFourieranalysishistoryitisaneme’fgjngdisciplinew

2、hichdevelpoedrapidlyintherecentyearsitsapplicationdomainisveryextensive，includingmanymatematiesdisciplines，signalanalysis，pictureprocessing，quantummechanicsandsoonmanyaspectsNowitisamaintoolinwaveletanalysisFametheoryder

3、ivesfromthesignalprocessingIn1952，DuffinandShafferintroducedtheconceptofframeforHilbertspacesinordertostudysomedeepprobleminnonharmonicFourierseriesWhenwavelettheoryisboomingDaubechies，GrossmanandMeyerconnectedcontinuous

4、wavelettransformswithframestheoryandintroducedwaveletframesTodayframestheoryhavebeenwidelyusedinwaveletanalysis，signalanalysis，imageprocessing，numericalanalysis，BanachspacestheoryetcThispapermainlytalksaboutthetheoryoffr

5、ameandpurtabationtheroyofflameTheresultsthatarequotedinthispaperaremostlyclassicalconclusionsorthenewestconclusionswhichshowtheresearchlevelandthedevelopingdirectionOnthebasisoftheresults，thispapergeneralizessomeresultsa

6、ndgivessomenewresultsThispaperiscomposedoffourparts：Thechapter1isallintroductionwhichsummarizestheemergence，developmentofwaveletanalysisandflamestheoryThechapter2presentsthebasicpropertiesofflameTheflameisaspecialBessels

7、equence，whichextendstheParsevalequalityoforthonormalbasisinHilbertspacetothetwosidedinequalityingeneralsequenceForeveryv，∈H，wehavef=∑((，，S1正)q)五，herek)嗣ER(T)1isthenoisedataThisshowsthe面framedecompositionhavesomeresistanc

8、etothenoiseWiththeredundancyofframeincreasingtheresistancewillbecomestrongerThereforeitisnecessarytodiscusstheframepropertiesThefirstpartinthechapter3studiesstabalityofframeandwaveletflameinL2(R)Thewaveletframeisaspecial

9、sequencewhichisaframeforL2(R)Thesequenceisacquiredbyaspecialfunctionactedbytwotransforms：dilationoperator吃withrealparameteral，nEZandtranslationoperator‰withrealparameter6o，mEZThefourthchapterdividesintotwoparts，thefirstp