Exercise 2.  Use  [Graphics:Images/ZTransformIntroModHome_gr_50.gif]   and   [Graphics:Images/ZTransformIntroModHome_gr_51.gif]   and prove that   [Graphics:Images/ZTransformIntroModHome_gr_52.gif].  

Solution 2.

See text and/or instructor's solution manual.

                    [Graphics:../Images/ZTransformIntroModHome_gr_53.gif]  

 

We are done.   

Aside.  We can let Mathematica double check our work.

 

[Graphics:../Images/ZTransformIntroModHome_gr_54.gif]

[Graphics:../Images/ZTransformIntroModHome_gr_55.gif]


[Graphics:../Images/ZTransformIntroModHome_gr_56.gif]

[Graphics:../Images/ZTransformIntroModHome_gr_57.gif]


[Graphics:../Images/ZTransformIntroModHome_gr_58.gif]

[Graphics:../Images/ZTransformIntroModHome_gr_59.gif]

Aside.  We can use Mathematica's ZTransform subroutine.

 

[Graphics:../Images/ZTransformIntroModHome_gr_60.gif]

[Graphics:../Images/ZTransformIntroModHome_gr_61.gif]

To get the desired form of the answer the numerator and denominator must be simplified.

 

[Graphics:../Images/ZTransformIntroModHome_gr_62.gif]

[Graphics:../Images/ZTransformIntroModHome_gr_63.gif]

          The Maple code is similar

[Graphics:../Images/ZTransformIntroModHome_gr_64.gif]  

                                                            [Graphics:../Images/ZTransformIntroModHome_gr_65.gif]

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell