Example 9.17 (b).  Use z-transform methods to solve  [Graphics:Images/ZTransformDEMod_gr_282.gif]   with  [Graphics:Images/ZTransformDEMod_gr_283.gif].  

[Graphics:../Images/ZTransformDEMod_gr_352.gif]

Explore Solution  9.17 (b).

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

[Graphics:../Images/ZTransformDEMod_gr_337.gif]




[Graphics:../Images/ZTransformDEMod_gr_338.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_339.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_340.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_341.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_342.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_343.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_344.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_345.gif]  with  [Graphics:../Images/ZTransformDEMod_gr_346.gif]  and  [Graphics:../Images/ZTransformDEMod_gr_347.gif].

[Graphics:../Images/ZTransformDEMod_gr_348.gif]




[Graphics:../Images/ZTransformDEMod_gr_349.gif]

[Graphics:../Images/ZTransformDEMod_gr_350.gif]

 

 

 

[Graphics:../Images/ZTransformDEMod_gr_351.gif]




[Graphics:../Images/ZTransformDEMod_gr_352.gif]

[Graphics:../Images/ZTransformDEMod_gr_353.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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