Example 9.24.  The moving average filter     
is designed to zero out  .

Explore Solution 9.24.

Use the conjugate pairs of zeros  ;  ;     and the additional zero    and calculate

The transfer function has the form   and we see that  .    The desired filter is  

To obtain the moving average filter use   for .  

As a typical example, we substitute   into the filter.

Remark 9.16. This is an extension of the filter in Example 9.23 (b), and zeros out twice as many frequencies.  The function has additional zeros located at  .  The transfer function can be written  
        .  
The representation and has a pole of order seven at the origin.  Also, as in the previous example the zeros are equally spaced points on the unit circle, and their arguments correspond to frequencies that are zeroed out by the filter.

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