信号与线性系统分析基础 课件5.4The Zero-Input Response and The Zero-State Response.ppt

信号与系统SignalsandSystems吉林大学

TheZero-InputResponse

and

TheZero-StateResponse

TheZero-InputResponseCharacteristicequation?j,(j=1,2,3,?,n)CharacteristicrootZero-InputResponseyzi(0)，yzi(1)，…，yzi(n-1)y(-1)，y(-2)，…，y(-n)yzi(k)=y(k)-yzs(k)=y(k)，k0Initialcondition

Characteristicequation:Characteristicroots:Zero-InputResponse:Example:TheZero-InputResponsey(k)+3y(k-1)+2y(k-2)=f(k),f(k)=2kε(k),y(-1)=0,y(-2)=1/2.Findyzi(k),k≥0.yzi(k)+3yzi(k-1)+2yzi(k-2)=0

TheZero-StateResponseCharacteristicequation?j (j=1,2,3,?,n)Characteristicroot(distinctroots?j)Zero-StateResponseyzs(-1)=yzs(-2)=…=yzs(-n)=0Initialstateyzs(0)，yzs(1)，…，yzs(n-1)Initialcondition