Example 9.16 (b).  Use z-transform methods to solve  [Graphics:Images/ZTransformDEMod_gr_216.gif]   with  [Graphics:Images/ZTransformDEMod_gr_217.gif].  

[Graphics:../Images/ZTransformDEMod_gr_278.gif]

Explore Solution 9.16 (b).

It is worthwhile to point out how Mathematica can do the important step using residues.

[Graphics:../Images/ZTransformDEMod_gr_263.gif]




[Graphics:../Images/ZTransformDEMod_gr_264.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_265.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_266.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_267.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_268.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_269.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_270.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_271.gif]  with  [Graphics:../Images/ZTransformDEMod_gr_272.gif]  and  [Graphics:../Images/ZTransformDEMod_gr_273.gif].

[Graphics:../Images/ZTransformDEMod_gr_274.gif]




[Graphics:../Images/ZTransformDEMod_gr_275.gif]

[Graphics:../Images/ZTransformDEMod_gr_276.gif]

 

 

 

[Graphics:../Images/ZTransformDEMod_gr_277.gif]




[Graphics:../Images/ZTransformDEMod_gr_278.gif]

[Graphics:../Images/ZTransformDEMod_gr_279.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell