信号与线性系统分析基础 课件5.3Linear input output difference equations with constant coefficients.ppt

信号与系统SignalsandSystems吉林大学

Linearinput/outputdifferenceequationswithconstantcoefficients

Input:f(k)=0fork0InitialCondition：y(0),y(1),y(2),…,y(n-1)InitialState：y(-1),y(-2),…,y(-n)Linearinput/outputdifferenceequationswithconstantcoefficientsEquation:Solution:

Linearinput/outputdifferenceequationswithconstantcoefficientsTheHomogeneousSolutionHomogeneousequationCharacteristicequationCharacteristicroot ?j(j=1,2,3,?,n)Homogeneoussolution

Linearinput/outputdifferenceequationswithconstantcoefficientsTheHomogeneousSolutionExample:y(k)+3y(k-1)+2y(k-2)=f(k),f(k)=2k,k≥0,y(0)=0,y(1)=2.Findyh(k).Characteristicequation:HomogeneousequationCharacteristicequationCharacteristicroot ?j(j=1,2,3,?,n)Homogeneoussolution

Linearinput/outputdifferenceequationswithconstantcoefficientsTheParticularSolution

Linearinput/outputdifferenceequationswithconstantcoefficientsTheParticularSolutionExample:y(k)+3y(k-1)+2y(k-2)=f(k),f(k)=2k,k≥0,y(0)=0,y(1)=2.Findyp(k),k≥0.Letyp(k)=P·2k,k≥0Substitutethesystemequation: