Example 9.15 (b).  Use z-transform methods to solve  [Graphics:Images/ZTransformDEMod_gr_150.gif]   with  [Graphics:Images/ZTransformDEMod_gr_151.gif].  

[Graphics:../Images/ZTransformDEMod_gr_212.gif]

Explore Solution 9.15 (b).

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

[Graphics:../Images/ZTransformDEMod_gr_197.gif]




[Graphics:../Images/ZTransformDEMod_gr_198.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_199.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_200.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_201.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_202.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_203.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_204.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_205.gif]  with  [Graphics:../Images/ZTransformDEMod_gr_206.gif]  and  [Graphics:../Images/ZTransformDEMod_gr_207.gif].

[Graphics:../Images/ZTransformDEMod_gr_208.gif]




[Graphics:../Images/ZTransformDEMod_gr_209.gif]

[Graphics:../Images/ZTransformDEMod_gr_210.gif]

 

 

 

[Graphics:../Images/ZTransformDEMod_gr_211.gif]




[Graphics:../Images/ZTransformDEMod_gr_212.gif]

[Graphics:../Images/ZTransformDEMod_gr_213.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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