Exercise 6.  Show that the convolution of the sequences      is   ,   

and that   .  

Solution 6.

See text and/or instructor's solution manual.

Let   ,   then the convolution is    

                      

Next, using      and      we have  

                      

On the other hand,

                      
    
Therefore,  

                    .  

We are done.   

Aside.  We can let Mathematica double check our work.

The convolution of    is    

The z-transforms of    are    

          The Maple code is similar

  

                                                            


  

                                                            


  

                                                            

This solution is complements of the authors.

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