Exercise 10.  Use direct substitution and trigonometric identities to show the following:  

10 (a).     will filter out the sequences      and   .  

Solution 10 (a).

See text and/or instructor's solution manual.

        Use   ,   and trigonometric identities  

                       and   

                    .  

Substitution reveals that  

                      

        Use   ,   and trigonometric identities

                       and   

                    .  

Substitution reveals that  

                      

We are done.   

Aside.  We can let Mathematica double check our work.

          The Maple commands are similar  

  

                                                            


  

                                                            

We are really done.   

          The Maple commands are similar  

  

                                                            


  

                                                            

This solution is complements of the authors.

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