《信号与线性系统分析基础 》 课件 6.5 卷积和与 LTI 离散系统的零状态响应

信号与系统SignalsandSystems吉林大学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.信号与系统SignalsandSystems吉林大学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信号与系统SignalsandSystems吉林大学z-DomainAnalysis—BlockDiagramRepresentationofDiscrete-timeSystemsinthez-DomainBlockDiagramRepresentationofDiscrete-timeSystems