工程数字信号处理72信号的时频分析

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1、信号的时频分析WavelettransformandFilterBankContinuouswavelettransformispowerful,butthecomputationamountofthecontinuouswavelettransformisverylarge.ItisliketousethecontinuousFouriertransformtocomputethespectrumofasignal.Forpracticalcomputingandapplication,thewavelettransformcanbediscr

2、etizedbysamplingboththescaleparametersandthetranslationparametert.信号的时频分析Inordertobuildacompleterepresentation,thediscretesequenceofscalemustensurethattheband-passofcancoverallthefrequency.Thediscretewavelettransformtakestheform信号的时频分析Modelofthemulti-frequencychannelseparatio

3、nofthewavelettransform信号的时频分析Modeloftherecursiveseparationofthewavelettransform信号的时频分析wherethewaveletisdefinedandgeneratedbyapairofdigitalfilter:信号的时频分析信号的时频分析Dimx(2048),y(2048),z(2048)ForK=5To500dt=1.0/5120z(k)=0.031274*y(k-ForK=0To2047x(k)=0.00000015)+0.010153*y(k-4)-y(k)=0

4、.00000010.051911*y(k-3)-z(k)=0.00000010.144445*y(k-2)-Next0.230024*y(k-x(255)=8.000ForK=5To5001)+0.734761*y(k)-y(k)=0.020828*x(k-0.230024*y(k+1)-5)+0.021483*x(k-4)-0.144445*y(k+2)-0.066692*x(k-3)-0.051911*y(k+3)+0.0101530.040838*x(k-2)+0.301233*x(k-*y(k+4)+0.031274*y(k+5)1)+0

5、.551253*x(k)+0.301233*xNext(k+1)-0.040838*x(k+2)-0.066692*x(k+3)+0.021483*x(k+4)+0.020828*x(k+5)Next信号的时频分析Thefilterbaseddiscretewavelettransformtakestheformwhereisthesmoothcoefficients,isthewaveletcoefficients,istheimpulseresponsecoefficientsofthelow-passfilter,istheimpulser

6、esponsecoefficientsofthehigh-passfilter.Andthereis信号的时频分析DiscreteDyadicWaveletTransformHowtodesignthefilterbankisthekeyofthefilterbasedthewavelettransform.Mallatgivesadigitalfilterbankandafastalgorithmofthediscretedyadicwavelettransform.Inthediscretedyadicwavelettransform,the

7、scaledilationofthewaveletisj=1,2,…….,NInthisscaledilation,onlyonepairofthefundamentalhalfbandfilterneedstobedesigned.信号的时频分析Theimpulseresponsecoefficientsofotherfiltersandcanbeobtainedbyinsertingzerosbetweeneachimpulseresponsecoefficientsofthefilterandthefilterseparately.Fore

8、xample:h1:h2:-0.120749-0.1207490.7532680.206415000.7532680.2064150.2