Unstable recursive equation
Clear memory
![[Graphics:../Images/index_gr_49.gif]](../Images/index_gr_49.gif)
Define difference equation and initial conditions
![[Graphics:../Images/index_gr_50.gif]](../Images/index_gr_50.gif)
![[Graphics:../Images/index_gr_51.gif]](../Images/index_gr_51.gif)
Simulated output for impulse input
Input
![[Graphics:../Images/index_gr_52.gif]](../Images/index_gr_52.gif)
![[Graphics:../Images/index_gr_53.gif]](../Images/index_gr_53.gif)
Output
![[Graphics:../Images/index_gr_54.gif]](../Images/index_gr_54.gif)
![[Graphics:../Images/index_gr_55.gif]](../Images/index_gr_55.gif)
Theoretical solution
Compute z-transform and transfer function
![[Graphics:../Images/index_gr_56.gif]](../Images/index_gr_56.gif)
![[Graphics:../Images/index_gr_57.gif]](../Images/index_gr_57.gif)
![[Graphics:../Images/index_gr_58.gif]](../Images/index_gr_58.gif)
![[Graphics:../Images/index_gr_59.gif]](../Images/index_gr_59.gif)
![[Graphics:../Images/index_gr_60.gif]](../Images/index_gr_60.gif)
![[Graphics:../Images/index_gr_61.gif]](../Images/index_gr_61.gif)
Compute poles of impulse response transfer function
![[Graphics:../Images/index_gr_62.gif]](../Images/index_gr_62.gif)
![[Graphics:../Images/index_gr_63.gif]](../Images/index_gr_63.gif)
Plot pole locations
![[Graphics:../Images/index_gr_64.gif]](../Images/index_gr_64.gif)
![[Graphics:../Images/index_gr_65.gif]](../Images/index_gr_65.gif)
Analytic impulse response
![[Graphics:../Images/index_gr_66.gif]](../Images/index_gr_66.gif)
![[Graphics:../Images/index_gr_67.gif]](../Images/index_gr_67.gif)
Converted by Mathematica
January 28, 2003