Example 9.15 (a).  Use z-transform methods to solve  [Graphics:Images/ZTransformDEMod_gr_148.gif]   with  [Graphics:Images/ZTransformDEMod_gr_149.gif].  

[Graphics:../Images/ZTransformDEMod_gr_195.gif]

Explore Solution 9.15 (a).

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

[Graphics:../Images/ZTransformDEMod_gr_170.gif]




[Graphics:../Images/ZTransformDEMod_gr_171.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_172.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_173.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_174.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_175.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_176.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_177.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_178.gif]  with   [Graphics:../Images/ZTransformDEMod_gr_179.gif].

[Graphics:../Images/ZTransformDEMod_gr_180.gif]




[Graphics:../Images/ZTransformDEMod_gr_181.gif]

[Graphics:../Images/ZTransformDEMod_gr_182.gif]

 

 

 

    To solve  [Graphics:../Images/ZTransformDEMod_gr_183.gif]   with  [Graphics:../Images/ZTransformDEMod_gr_184.gif],  we will use our Mathematica subroutine  [Graphics:../Images/ZTransformDEMod_gr_185.gif]  for finding the solution to  [Graphics:../Images/ZTransformDEMod_gr_186.gif].   It will take the z-transforms of each term;  solve for  [Graphics:../Images/ZTransformDEMod_gr_187.gif];  and it's inverse [Graphics:../Images/ZTransformDEMod_gr_188.gif].   The format of the subroutine call is   [Graphics:../Images/ZTransformDEMod_gr_189.gif]  with   [Graphics:../Images/ZTransformDEMod_gr_190.gif].

[Graphics:../Images/ZTransformDEMod_gr_191.gif]




[Graphics:../Images/ZTransformDEMod_gr_192.gif]

[Graphics:../Images/ZTransformDEMod_gr_193.gif]

 

 

 

[Graphics:../Images/ZTransformDEMod_gr_194.gif]




[Graphics:../Images/ZTransformDEMod_gr_195.gif]

[Graphics:../Images/ZTransformDEMod_gr_196.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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