小波級數(shù)變換中初始尺度系數(shù)的計算.pdf

1、西安電子科技大學(xué)碩士學(xué)位論文小波級數(shù)變換中初始尺度系數(shù)的計算姓名：王亞軍申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：馮象初20030101ABSTRACTInsomeapplicationsofwavelets，suchassignalanalysisanddataprocessingetc，theexactcoefficientsofthecontinuouswaveletstransform(CWT)orofwaveletseries

2、transform(WST)areoftenneededHoweveritisverydifficulttocomputethewaveletexpansioncoefficientsofafunctionorasignaldirectlyInstead，theinitialscalecoemcientsofWSTarecomputedfirst，thenthewaveletexpansioncoefficiemsofafunction

3、orasignalarecomputedbyuseofMallat’SalgorithmThecomputationofinitialscalecoefficientsinthewaveletisstudiedinthedissertationTheprimarycontentsaresummarizedbelow：Wediscussthemomentofcascadeiterationfunctions玎””(x)andthemome

4、ntofscalingfunctions6p(x1Itisprovedthattheerrororderofthe，一momentofcascadeiterationfunctionandthet—momentofscalingfunctionis2“toanygiven1Basedonthisresult，theintegralvalueisestimatedThus，whentheerrorisunderthetolerance，C

5、anbeevaluatedapproximatelyby，thelatterCanbecalculatedfrombyuseofcascadealgorithmMoreoverintheperiodiecase，thesimilarresultsfor仿j：’@0and萬，I(x)isalsoobtainedInordertOgetoverthedrawbackoftheMallat’Salgorithm，F(xiàn)IRpreftlterwit

6、htheapproximationconditionisdiscussedanditsapproximationpropertyisanalyzedThenakindofFIRadaptivewaveletprefilterwithasingleparameterisdesignedtoobtaintheinitialscalecoefficientsfordiscretesignalsandforcontinualsignalsres