《信號(hào)與線性系統(tǒng)分析基礎(chǔ) 》 課件 第 3 章 連續(xù)時(shí)間信號(hào)的頻域分析

信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)IntroductionandtheBasicRepresentationofFourierSeriesTheBackgroundofFourierseriesFourierseries(F.S.forshort)isnamedaftertheFrenchmathematicianandphysicistJeanBaptistFourier(1768-1830),whowasthefirstonetoproposethatperiodicwaveformscouldberepresentedbyasumofsinusoids(orcomplexexponentials)inthepaperonheatconductionwhichwaspresentedtoParisAcademyofScience.Fourierwasalsoveryactiveinthepoliticsofhistime.Forexample,heplayedanimportantroleinNapoleon’sexpeditionstoEgyptduringthelate1790s.TheFourierseriesofperiodicsignals--trigonometricseriesTheF.S.intermsoftrigonometricseriesTheFourierseriesofperiodicsignals--harmonicsTheFourierseriesofperiodicsignals--harmonicsTheF.S.intermsofharmonics信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)ContributionofSymmetryoftotheFourierSeriesContributionofsymmetryoftotheF.S.(1)ContributionofsymmetryoftotheF.S.(2)ContributionofsymmetryoftotheF.S.(3)ContributionofsymmetryoftotheF.S.(4)(5)[Example]ContributionofsymmetryoftotheF.S.信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheFourierSeriesintermsofPeriodicComplexExponentialsTheF.S.intermsofperiodiccomplexexponentialsTheFourierseriesofperiodicsignals--periodiccomplexexponentialsTheF.S.intermsofperiodiccomplexexponentialsTheFourierseriesofperiodicsignals--periodiccomplexexponentials信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)FrequencySpectraofPeriodicSignalsFrequencyspectraofperiodicsignalsDefinition--Graphsthatfrequencycomponentsforaredisplayedbyverticallines.Description1Howtoplotfrequencyspectra2FrequencyspectraofperiodicsignalsUnilateralspectraBilateralspectraFrequencyspectraofperiodicsignalsExercise:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheFourierSeriesofaRectangularPulseTrainTheFourierseriesofarectangularpulsetrain1TheFourierseriesofarectangularpulsetrain2TheFourierseriesofarectangularpulsetrain2信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)FourierTransformandInverseFourierTransformFouriertransformofanaperiodicsignalISpectraldensityfunctionFouriertransformofanaperiodicsignalⅡFouriertransformandinverseFouriertransformFouriertransformofanaperiodicsignal信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)CommonFourierTransformPairs(1)CommonFouriertransformpairs12CommonFouriertransformpairs3CommonFouriertransformpairs4CommonFouriertransformpairs5CommonFouriertransformpairs6信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty1:LinearityProperty1:LinearityProof:[Example]Property1:Linearity信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty2:DualityProperty2:DualityProof:[Example]Property2:Duality信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty3:MultiplicationbyacomplexexponentialProof:Property3:MultiplicationbyacomplexexponentialMultiplicationbyacomplexexponential(shiftinfrequency)Property3:Multiplicationbyacomplexexponential(1)Inferences:ModulationtheoremModulatingsignalCarriersignalModulatedsignalProperty3:MultiplicationbyacomplexexponentialProperty3:Multiplicationbyacomplexexponential信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty4:ShiftintimeProperty5:TimescalingProperty4:ShiftintimeProof:Property5:TimescalingProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty6:ConjugationandConjugateSymmetryProperty6:ConjugationandConjugateSymmetry(1)Property6:ConjugationandConjugateSymmetry(1)Property6:ConjugationandConjugateSymmetry(2)Property6:ConjugationandConjugateSymmetry(2)Property6:ConjugationandConjugateSymmetry(3)信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty7&8:ConvolutionTheoremsProperty7:Convolutioninthet-domainProof:Property8:Multiplicationinthet-domainMultiplicationinthet-domain(Convolutionintheω-domain)Proof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty9:Differentiationinthetime-domainProperty9:Differentiationinthetime-domainProof:(Suitabletotime-limitedsignals)信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty10:Integrationinthet-domainProperty10:Integrationinthet-domainProof:Property10:Integrationinthet-domainProperty10:Integrationinthet-domainProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofFourierTransformProperty11&12:DifferentiationandIntegrationintheω-DomainProperty11:Differentiationintheω-domainProof:Example:Property11:Differentiationintheω-domainProperty12:Integrationintheω-domain信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheFourierTransformofaPeriodicSignalTheFouriertransformofaperiodicsignalⅠF.T.ofanon-sinusoidalperiodicsignalⅡTherelationshipbetweenandExample:TheFouriertransformofaperiodicsignal信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)Steady-StateResponsetoNon-SinusoidalPeriodicSignalsSteady-stateresponsetonon-sinusoidalperiodicsignalsExample:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)FrequencyResponseFunction(SystemFunction)Frequencyresponsefunction(systemfunction)1.DefinitionFrequencyresponsefunction(systemfunction)Example:Findthesystemfunctionofthecircuitgivenbelow.信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)ResponsetoAperiodicSignalsResponsetoaperiodicsignalsExample:Responsetoaperiodicsignals信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)AnalysisofDistortionlessSystemsAnalysisofdistortionlesssystemsⅠDistortionlesssystemAnalysisofdistortionlesssystemsⅡThenecessaryandsufficientconditionofdistortionlesstransmission信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)AnalysisofIdealLowpassFilters(ILFs)Analysisofideallowpassfilters(ILFs)ⅠThecharacteristicofILFsⅡTheimpulseresponseofILFAnalysisofideallowpassfilters(ILFs)ⅢTheapproximatelydistortionlessconditionofILFsAnalysisofideallowpassfilters(ILFs)ⅣPhysicalrealizabilityofasystemAnalysisofideallowpassfilters(ILFs)——Paley-WienercriterionIntime-domainInfrequency-domain信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)SamplingandtheFourierTransforms(FTs)ofSampledContinuous-TimeSignalsSamplingandtheFouriertransformofⅠSamplingprocessAsamplingprocessisto“extract”aseriesofdiscretesamplevaluesfromacontinuous-timesignalbyusingasamplingimpulse(orpulse)train.ⅡClassification

Impulse-trainsampling(idealize