《信號(hào)與線性系統(tǒng)分析基礎(chǔ) 》 課件 第 4 章 連續(xù)時(shí)間系統(tǒng)的頻域分析

信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)DefinitionsofLaplaceTransformandInverseLaplaceTransformDefinitionsofLaplacetransform(LT)andinverseLTFromFouriertransformtoLaplacetransformⅠTheLaplacetransform(LTforshort)ⅡOne-sided(unilateral)LT:Two-sided(bilateral)LT:DefinitionsofLaplacetransform(LT)andinverseLTⅢ信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheRegionofConvergence(ROC)forLaplaceTransformsTheROCoftheLaplacetransform[Example]TheROCoftheLaplacetransformTherangeofvaluesofsforwhichtheintegralinconvergesisreferredtoastheregionofconvergence(ROC)oftheLaplacetransform(LT).Theregionofconvergence(ROC)oftheLTf(t)isintegrablewithin(a,b)(1)(0≤a<b<∞)Foranarbitraryσ0,(2)信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)CommonLaplaceTransformpairsCommonLaplacetransformpairsCommonone-sidedLTpairsCommonLaplacetransformpairs[Example]信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform:LinearityandShiftinthes-DomainProperty1：LinearityProof:Property2：Shiftinthes-domainProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplacetransform:RightShiftinTimeProperty3:RightshiftintimeProof:Property3:Rightshiftintime(3)Property3:RightshiftintimeSolution:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform:TimeScalingProperty4:TimescalingProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform:ConvolutionTheoremsProperty5:Convolutioninthet-domainProof:Property5:Convolutioninthet-domainContinued:Property

6:Convolutioninthes-domainProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform:Differentiationinthet-domainProperty7:Differentiationinthet-domainProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform:Integrationinthet-domainProperty8:Integrationinthet-domainProof:Property8:Integrationinthet-domain信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform:DifferentiationandIntegrationinthes-DomainProperty9:Differentiationinthes-domainProof:Property10:Integrationinthes-domainProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)PropertiesofLaplaceTransform：InitialandFinal-ValuetheoremsProperty11：Initial-valuetheoremProof:Property12：Final-valuetheoremProof:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)ComputationoftheInverseLaplaceTransform(Ⅱ)PartialFractionExpansionComputationoftheinverseLaplacetransform(Ⅱ)Partialfractionexpansion(1)Conditions:ComputationoftheinverseLaplacetransform(Ⅱ)Partialfractionexpansion(2)ComputationoftheinverseLaplacetransform(Ⅱ)Partialfractionexpansion(3)信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)SolvingtheDifferentialEquationsinthes-DomainSolvingthedifferentialequationsinthes-domain[Example]Given:Find：

Solvingthedifferentialequationsinthes-domainSolvingthedifferentialequationsinthes-domainSolvingthedifferentialequationsinthes-domain信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)Thes-DomainRepresentationsofCircuits(I)Thes-domainrepresentationsofcircuits(I)1Thes-domainequivalentcircuitelementsThesameresistanceThes-domainrepresentationsofcircuits(I)1Thes-domainequivalentcircuitelementsThes-domainimpedanceThes-domainrepresentationsofcircuits(I)1Thes-domainequivalentcircuitelementsThes-domainimpedanceThes-domainrepresentationsofcircuits(I)2TheformsofKVLandKCLinthes-domain信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheBlockDiagramofaSysteminthes-DomainTheblockdiagramofasysteminthes-domainScalarmultiplier1Adder/Subtractor2Theblockdiagramofasysteminthes-domainIntegrator3信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheDefinitionofTransferFunctionanditsSolutionsThedefinitionoftransferfunctionanditssolutionsThetransferfunctionⅠHowtofind21.GiventhesystemdifferentialequationThedefinitionoftransferfunctionanditssolutionsHowtofind21.GiventhesystemdifferentialequationThedefinitionoftransferfunctionanditssolutions2.Giventheimpulseresponseh(t)Thedefinitionoftransferfunctionanditssolutions3.GiventhestructureofthecircuitUsingthedefinitioninthes-domainrepresentationofthecircuit.4.Usingthepole-zeroplot信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)TheTransferFunctionandthePole-ZeroPlotThetransferfunctionandthepole-zeroplotPolesandzeros1Zeros:Poles:Thetransferfunctionandthepole-zeroplotThepole-zeroplot2Aplotinthecomplexplaneshowingthelocationsofallthepoles(markedby×)andallthezeros(markedby○)iscalledthepole-zeroplot.Zeros:Poles:信號(hào)與系統(tǒng)SignalsandSystems吉林大學(xué)ApplicationsofthePole-ZeroPlot:DeterminingtheFormofh(t)Thepoles

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left-halfcomplexplane1Applicationsofthepole-zeroplot:Determiningtheformofh(t)Thepoles

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left-halfcomplexplane1Applicationsofthepole-zeroplot:Determiningtheformofh(t)Thepoles

beinglocatedattheorigin2Applicationsofthepole-zeroplot:Determin