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弹丸回波信号的瞬时频率估计.docx

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弹丸回波信号的瞬时频率估计 Introduction: Insignalprocessing,theestimationofinstantaneousfrequencyisaveryimportanttechniqueasithaswideapplicationsinvariousfieldssuchascommunication,neuroscience,radar,sonar,speechprocessing,andmanymoreareas.InstantaneousfrequencyestimationtechniquesareutilizedtoanalyzethefrequencychangesofatimevaryingsignalwhichcannotbecompletelydescribedbyitsFouriertransform. Inthispaper,wewilldiscusstheestimationofinstantaneousfrequencyofasignalusingthemethodofHilbert-Huangtransform.Wewillspecificallyapplythismethodtoanalyzeechocardiogramsignals,particularlytheDopplersignalscreatedbytheheart.TheinstantaneousfrequencyestimationoftheDopplersignalscanbeusedtoobtainimportantinformationaboutthecardiovascularsystem. Section1:TheoreticalBackground Toestimatetheinstantaneousfrequencyofasignal,weneedtofirstunderstandtheconceptoftheanalyticsignal.Ananalyticsignalisacomplexsignalthatconsistsoftheoriginalsignalandanimaginarysignalwithaphaseshiftof90degrees.Inotherwords,itisthesumoftheoriginalsignalandasignalthatis90degreesoutofphasewiththeoriginalsignal. TheHilberttransformisamathematicaltechniqueusedtoconstructananalyticsignalfromagivenrealsignal.ItisrepresentedbyH(f),anditoperatesontheFouriertransformofthesignal.TheHilberttransformisdefinedastheconvolutionoftheoriginalsignalf(t)withthefunction: h(t)=(1/πt)t≠0 h(t)=0t=0 Theanalyticsignalcanthenberepresentedas: z(t)=f(t)+iH(f(t)) whereiistheimaginaryunit. Thenextstepistoextracttheinstantaneousfrequencyfromtheanalyticsignal.Itcanbedefinedasthetimederivativeoftheinstantaneousphaseφ(t): ω(t)=dφ(t)/dt Theinstantaneousphaseφ(t)isobtainedbytakingthearctangentoftheratiooftheimaginarypartandtherealpartoftheanalyticsignal: φ(t)=tan−1(Im[z(t)]/Re[z(t)]) Section2:ApplicationstoEchocardiogramSignals Echocardiogramsignalsareusedtoobtaininformationaboutthecardiovascularsystem,includingthefunctioningoftheheartandthecirculatorysystem.Dopplersignalscanbemeasuredusingultrasoundtechniques,whichcanprovideinformationaboutthebloodflowintheheart.