Example 9.16 (a).  Use z-transform methods to solve  [Graphics:Images/ZTransformDEMod_gr_214.gif]   with  [Graphics:Images/ZTransformDEMod_gr_215.gif].  

[Graphics:../Images/ZTransformDEMod_gr_261.gif]

Explore Solution 9.16(a).

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

[Graphics:../Images/ZTransformDEMod_gr_236.gif]




[Graphics:../Images/ZTransformDEMod_gr_237.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_238.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_239.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_240.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_241.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_242.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_243.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_244.gif]  with   [Graphics:../Images/ZTransformDEMod_gr_245.gif].

[Graphics:../Images/ZTransformDEMod_gr_246.gif]




[Graphics:../Images/ZTransformDEMod_gr_247.gif]

[Graphics:../Images/ZTransformDEMod_gr_248.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_249.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_250.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_251.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_252.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_253.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_254.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_255.gif]  with   [Graphics:../Images/ZTransformDEMod_gr_256.gif].

[Graphics:../Images/ZTransformDEMod_gr_257.gif]




[Graphics:../Images/ZTransformDEMod_gr_258.gif]

[Graphics:../Images/ZTransformDEMod_gr_259.gif]

 

 

 

[Graphics:../Images/ZTransformDEMod_gr_260.gif]




[Graphics:../Images/ZTransformDEMod_gr_261.gif]

[Graphics:../Images/ZTransformDEMod_gr_262.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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