Exercise 4.  Find and simplify over a common denominator the following z-transforms.

4 (a).  .

Solution 4 (a).

See text and/or instructor's solution manual.

Answer.   .  

Solution.   Use the facts      and      and linearity, and Table 9.1.  

                      

Therefore,

                    .  

We are done.   

Aside.  We can use Definition 9.1 and let Mathematica double check our work.

          The Maple code is similar

  

                                                            

We are really done.   

Aside.  We can use Mathematica's ZTransform subroutine.

          The Maple code is similar

  

                                                            

We are really really done.   

Aside.  We can graph some of the terms in the sequence.

                                                                                                                        The sequence   .   

This solution is complements of the authors.

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