Marginally stable recursive equation
Clear memory
![[Graphics:../Images/index_gr_68.gif]](../Images/index_gr_68.gif)
Define difference equation and initial conditions
![[Graphics:../Images/index_gr_69.gif]](../Images/index_gr_69.gif)
![[Graphics:../Images/index_gr_70.gif]](../Images/index_gr_70.gif)
Simulated output for impulse input
Input
![[Graphics:../Images/index_gr_71.gif]](../Images/index_gr_71.gif)
![[Graphics:../Images/index_gr_72.gif]](../Images/index_gr_72.gif)
Output
![[Graphics:../Images/index_gr_73.gif]](../Images/index_gr_73.gif)
![[Graphics:../Images/index_gr_74.gif]](../Images/index_gr_74.gif)
Theoretical solution
Compute z-transform and transfer function
![[Graphics:../Images/index_gr_75.gif]](../Images/index_gr_75.gif)
![[Graphics:../Images/index_gr_76.gif]](../Images/index_gr_76.gif)
![[Graphics:../Images/index_gr_77.gif]](../Images/index_gr_77.gif)
![[Graphics:../Images/index_gr_78.gif]](../Images/index_gr_78.gif)
![[Graphics:../Images/index_gr_79.gif]](../Images/index_gr_79.gif)
![[Graphics:../Images/index_gr_80.gif]](../Images/index_gr_80.gif)
Compute poles of impulse response transfer function
![[Graphics:../Images/index_gr_81.gif]](../Images/index_gr_81.gif)
![[Graphics:../Images/index_gr_82.gif]](../Images/index_gr_82.gif)
Plot pole locations
![[Graphics:../Images/index_gr_83.gif]](../Images/index_gr_83.gif)
![[Graphics:../Images/index_gr_84.gif]](../Images/index_gr_84.gif)
Analytic impulse response
![[Graphics:../Images/index_gr_85.gif]](../Images/index_gr_85.gif)
![[Graphics:../Images/index_gr_86.gif]](../Images/index_gr_86.gif)
![[Graphics:../Images/index_gr_87.gif]](../Images/index_gr_87.gif)
Converted by Mathematica
January 28, 2003