Stable recursive equation
Clear memory
![[Graphics:../Images/index_gr_88.gif]](../Images/index_gr_88.gif)
Define difference equation and initial conditions
![[Graphics:../Images/index_gr_89.gif]](../Images/index_gr_89.gif)
![[Graphics:../Images/index_gr_90.gif]](../Images/index_gr_90.gif)
Simulated output for impulse input
Input
![[Graphics:../Images/index_gr_91.gif]](../Images/index_gr_91.gif)
![[Graphics:../Images/index_gr_92.gif]](../Images/index_gr_92.gif)
Output
![[Graphics:../Images/index_gr_93.gif]](../Images/index_gr_93.gif)
![[Graphics:../Images/index_gr_94.gif]](../Images/index_gr_94.gif)
Theoretical solution
Compute z-transform and transfer function
![[Graphics:../Images/index_gr_95.gif]](../Images/index_gr_95.gif)
![[Graphics:../Images/index_gr_96.gif]](../Images/index_gr_96.gif)
![[Graphics:../Images/index_gr_97.gif]](../Images/index_gr_97.gif)
![[Graphics:../Images/index_gr_98.gif]](../Images/index_gr_98.gif)
![[Graphics:../Images/index_gr_99.gif]](../Images/index_gr_99.gif)
![[Graphics:../Images/index_gr_100.gif]](../Images/index_gr_100.gif)
Compute poles of impulse response transfer function
![[Graphics:../Images/index_gr_101.gif]](../Images/index_gr_101.gif)
![[Graphics:../Images/index_gr_102.gif]](../Images/index_gr_102.gif)
Plot pole locations
![[Graphics:../Images/index_gr_103.gif]](../Images/index_gr_103.gif)
![[Graphics:../Images/index_gr_104.gif]](../Images/index_gr_104.gif)
Analytic impulse response
![[Graphics:../Images/index_gr_105.gif]](../Images/index_gr_105.gif)
![[Graphics:../Images/index_gr_106.gif]](../Images/index_gr_106.gif)
![[Graphics:../Images/index_gr_107.gif]](../Images/index_gr_107.gif)
Converted by Mathematica
January 28, 2003