PAGE\*MERGEFORMAT31TimeFrequencyAnalysisandWaveletTransformTutorialTime-FrequencyAnalysisforBiomedicalEngineeringChia-JungChang(張嘉容)NationalTaiwanUniversityABSTRACTBiomedicalrelatedresearchrequireslotsofmathematicalandengineeringtechniquestoanalyzedata.Amongthesubfields,electrophysiologicalresearchplaysthecorerole.Inthistutorial,severaltoolsareexamined,includingelectrocardiogram,andelectroencephalogram.Thesearethemostcommontoolsusedtodiagnoseourphysiologicalactivitiessinceneuralresponsescarryinformation.Becausebiomedicalsignalsareusuallynonstationary,Fouriertransformisnotsuitabletoapplyhere.Besides,traditionalsignalsareanalyzedinfrequencydomain,separatelyfromtimedomain,suchthatextraordinaryconditionsarehardtobeobserved.Tosolvesuchproblem,time-frequencyanalysisandwavelettransformprovidebothtimeandfrequencyinformationsimultaneously.Inthefollowingtutorial,Iwouldliketotalkaboutthetheoreticalbackgroundofbothtime-frequencyanalysisandwavelettransformmethods,includingwhatpropertiestheyhave,theircommontypes,andhowtooperatethem.Secondly,IwouldbrieflyintroducethreecommonphysiologicaltoolssuchasECG,andEEG.Wheretheycanbeapplied,whattheyaretargeting,andwhatanalysismethodscanbeused,andhowtheyperformwillbedescribed.CONTENTSAbstractTheoreticalBackgroundTime-FrequencyAnalysisMethodsCohen’sClassDistributionFourDerivativeDistributionsElectrophysiologicalApplicationsWaveletTransformFromFouriertoWaveletTransformFourierTransformShortTimeFourierTransformWaveletTransformContinuousWaveletTransformPropertiesRepresentativeSignalsDiscreteWaveletTransformPropertiesRepresentativeSignalsSelectionofBaseWaveletforBiomedicalSignalsOverviewSelectionCriteriaBiomedicalApplicationsElectrocardiography(ECG)IntroductionMethodResultElectroencephalography(EEG)IntroductionMethodResultSummaryReferencesTime-FrequencyAnalysisMethodsGreatprogresshasbeenmadeinapplyinglineartime-invarianttechniquesinsignalprocessing.Insuchcasesthedeterministicpartofthesignali