《信號與線性系統(tǒng)分析基礎(chǔ) 》 課件 6.5 卷積和與 LTI 離散系統(tǒng)的零狀態(tài)響應(yīng)

信號與系統(tǒng)SignalsandSystems吉林大學(xué)z-DomainAnalysis—TransformoftheInput/outputDifferenceEquationTransformoftheInput/outputDifferenceEquationLTIsystem:Input:f(k)=0,k<0Initialstate:y(-1),y(-2),…,y(-n)z-Transform:Y(z)=Yzi(z)+Yzs(z)IZT:y(k)=yzi(k)+yzs(k)TransformoftheInput/outputDifferenceEquationExample:y(k)-y(k-1)-2y(k-2)=f(k)+2f(k-2),y(-1)=2,y(-2)=-0.5,f(k)=e(k).Findyzi(k),yzs(k),y(k),k≥0.TransformoftheInput/outputDifferenceEquationExample:y(k)-y(k-1)-2y(k-2)=f(k)+2f(k-2),y(-1)=2,y(-2)=-0.5,f(k)=e(k).Findyzi(k),yzs(k),y(k),k≥0.TransformoftheInput/outputDifferenceEquationExample:y(k)-y(k-1)-2y(k-2)=f(k)+2f(k-2),y(-1)=2,y(-2)=-0.5,f(k)=e(k).Findyzi(k),yzs(k),y(k),k≥0.信號與系統(tǒng)SignalsandSystems吉林大學(xué)z-DomainAnalysis—TheSystemFunctionTheSystemFunction(TransferFunction)DefinitionDeterminationofthesystemfunction(1)

H(z)=Yzs(z)/F(z)(2)H(z)=Z[h(k)]SystemFunctionofInterconnectionsSeriesconnectionH(z)ParallelconnectionH(z)Parallelconnection

H(z)SystemFunctionforInterconnectionsofLTISystemsExample:Determinethezero-stateoftheLTIsystem.Pole-zeroPlotoftheSystemFunctionPole-zeroplotExample:Aplotofthelocationsinthecomplexplaneofthepolesandzeros.ZerosrootsofN(z)=0——○ZerosrootsofD(z)=0——×zeros:z=0poles:z=1信號與系統(tǒng)SignalsandSystems吉林大學(xué)z-DomainAnalysis—BlockDiagramRepresentationofDiscrete-timeSystemsinthez-DomainBlockDiagramRepresentationofDiscrete-timeSystems