搜索
2003-04-11W0305011969-1000-58702004==============01-0127-05121.2570612.257061MATLABTN911A1--2FurierFTFTfxexpi～wx～w∈RfxFTFTfxFT^fwfxGabor1946FTFTFT2080FTfxFTexpi～wx～w∈RL22πψjkxE2-j2ψ2-jx-kjk∈ZL2R3ψ120HarrLittlewood-Raley2070CalderonHardy41982Stromberg2080MorletMeyer1986ψL2RMeyerMallatMRAMallat4Daubechies1988MRA--DBDBMallat1990--5200428Vol.28No.11JournaloftheUniversityofPetroleumChinaFeb.2004Cohen2Swelden6FTDaubechies1998722.1HaarShannon8HaarHaarHaarHaarShannonShannonHaarφtψtφShannontEsinπtπt.ψShannontEsinπt-12-sin2πt-12πt-12.φHaartE1t∈010t01.ψHaartEhtE10#t$12-112#t$10t$0t%1&’(.1HaarShannon1HaarShannon2.2Meyer3MeyerMeyerMRAMRAθuθuE0u#13θuEπ2u)23*u∈Rθu+θ1-uEπ2θudd%1θudMeyerφtFT^φwEcosθw^φwd^φwE1w#13^φwE0w%23.^φw-2323^φw+k^φw+k2E1^φ2wEm0w^φwE+k^φ2w+2k^φwMRAψED-1gTφψnETnψDT^ψ2wE-exp-2πiλw^φ2w-1+^φ2w+1^φw.IFTMeyerθuMeyerθuMeyer2821200422Meyer2.3DBMRA2.3.11L2RVjj∈ZL2R①=j∈ZVj⊂Vj-1②⋂j∈ZVjE0Uj∈ZVjEL2R③ux∈Vj⇔u2x∈Vj-1④=k∈Zux∈V0⇔ux-k∈V0⑤=g∈V0g2-jx-k|k∈ZV0Riesz2L2R=j∈ZWjVjVj-1Vj-1EVj⊕WjVjEVJ⊕⊕J-j-1kE0WJ-kL2RE⊕j∈ZWj.3φt∈V0φt-nn∈ZV0ψt∈W0ψt-nn∈ZW0DTφtψtDφEhTφDψEgTφhTE∑nhnTngTE∑ngnTnE-Tλh-T*.4hTgT∑nhnhn+2kEδ0kφt3ψtψtφtDBφtψt2.3.2DB23DB02N-1NE123NE1HaarN≥2DBφtψtNHölderﾍ2cnEﾍ2hndnEﾍ2gn.3DφEhTφ⇔φtEﾍ2∑nhnφ2t-nt∑nhnEﾍ2.4hz2+h-z2E2T→exp-2πiw≡z.PT≡12∑ncnTnE1ﾍ2hTQT≡12∑ndnTnE1ﾍ2gTE-TλP-T*P1E12∑ncnE1ﾍ2∑nhnE1Pz2+P-z2E1zEexp-2πiw╰╰.1PTc0M1∑MnE0cnE2∑M-2knE0cncn+2kE2δ0kkE01M2╰╰.2c0cM≠0M2c0cMME2N-1N≥1M2EN-122NN+1NE1N+1E2N2c0Ec1E1HaarN≥2N-12Nc0cM→h0hMφt3ψtN-1NDBN-1NE3DB39212813DB2.3.3501V0V0φtψtN1tEx01tE10≤t10t0t≥1.N2tEN1*N1tEʃ10N1uN1t-uduEt0≤t12-t1≤t20t0t≥2╰╰.N3tEN2*N1tEʃ10N1uN2t-uduEt220≤t134-t-3221≤t2t-3222≤t30t0t≥3╰╰.NmtENm-1t*N1tmNmtNmtNmt-nn∈ZNmtMRA3m2.49hg～h～g4～h～ghghz～hz-1+gz～gz-1E2.3hz～h-z-1+gz～g-z-1E0.44hgnew～hnew～g34liftinggnewzEgz+hzsz2～hnewzE～hz-gzsz-2.szLaurenthnewg～h～gnew34DualLifting～gnewzE～gz+～hzsz2hnewzEhz-gz~sz-2.~sz-2LaurentFIRLasyWavelet67sz~sz2.5MRA31021112131415216303120042HaarShannonMRAMallatDBMallat1DAUBECHIESI.TenLecturesonWaveletsM.Montpe-lierCapitalCityPress1992.2MALLATS.AWaveletTourofSignalProcessingM.SanDiegoAcademicPress1998.3KAISERG.AFriendlyGuidetoWaveletsM.Mas-sachusettsLowell1994.4.M.1995.5.M..1995.6SWELDENSW.BuildingyourownwaveletsathomeA.WSweldenssSelectedPublicationC.SanDiegoAcademicPress1996.17-88.7DAUBECHIESISWELDENSW.Facoringwavelettrans-formsintoliftingstepsJ.JournalFourierAnalApp19981-26.8.M.1997.9.R.2000.10.3J.A2001317602-614.11.D.2001.12.J.200034197-99.13MARTINVetterli.Waveletsapproximationandcom-pressionJ.IEEESignalProcessingMagazine200111359-73.14CALBERBANKARDAUBECHIESIandSWELDENSW.LosslessimagescompressionusingintegertointegerwavelettransformA.WSweldenssSelectedPublicationC.SanDiegoAcademicPress1998.178-206.15.J.200131422-26.16.4J.200024695-97.～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～～1261KUBICEKMandHALAVACEKV.NumericalSolutionofNonlinearBoundaryValueProblemswithApplicationsM.NewJerseyPrintice-HallINC1983.2ALLGOWERELandGEORGK.NumericalContinua-tionMethodsM.HeidelbergSpringer-Verlag1990.3GOLUBGHandVANLOANCF.MatrixComputa-tionsM.BaltimoreTheJohnsHopkinsUniversityPress1996.4.M.2001.5LIWeiguo.SolvingthePBVPwiththeinitialvalueproblemmethodJ.JournalofMathematicalAnalysis&Application1998261259-270.6LIWeiguoandSHENZuhe.Aconstructiveproofonex-istenceanduniquenessof2-piperiodicsolutionofDuffingequationJ.NonlinearAnalysis20004271209-1220.131281