Example 9.19.  Solve  [Graphics:Images/ZTransformDEMod_gr_400.gif]   with  [Graphics:Images/ZTransformDEMod_gr_401.gif].  

[Graphics:Images/ZTransformDEMod_gr_402.gif]

Explore Solution 9.19.

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

[Graphics:../Images/ZTransformDEMod_gr_417.gif]




[Graphics:../Images/ZTransformDEMod_gr_418.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_419.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_420.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_421.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_422.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_423.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_424.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_425.gif]  with   [Graphics:../Images/ZTransformDEMod_gr_426.gif].

[Graphics:../Images/ZTransformDEMod_gr_427.gif]




[Graphics:../Images/ZTransformDEMod_gr_428.gif]

[Graphics:../Images/ZTransformDEMod_gr_429.gif]

 

 

 

[Graphics:../Images/ZTransformDEMod_gr_430.gif]




[Graphics:../Images/ZTransformDEMod_gr_431.gif]

[Graphics:../Images/ZTransformDEMod_gr_432.gif]

[Graphics:../Images/ZTransformDEMod_gr_433.gif]

[Graphics:../Images/ZTransformDEMod_gr_434.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_435.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_436.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_437.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_438.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_439.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_440.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_441.gif]  with   [Graphics:../Images/ZTransformDEMod_gr_442.gif].

[Graphics:../Images/ZTransformDEMod_gr_443.gif]




[Graphics:../Images/ZTransformDEMod_gr_444.gif]

[Graphics:../Images/ZTransformDEMod_gr_445.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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