## Frequency Response

Given the transfer function , the frequency response is obtained by evaluating it on the unit circle in the complex plane, i.e., by setting , where is the sampling interval in seconds, and is radian frequency:4.3

 (4.4)

In the special case , we obtain

When , the frequency response is a ratio of cosines in times a linear phase term (which corresponds to a pure delay of samples). This special case gives insight into the behavior of the filter as its coefficients and approach 1.

When , the filter degenerates to which corresponds to ; in this case, the delayed input and output signals cancel each other out. As a check, let's verify this in the time domain:

Next Section:
Amplitude Response
Previous Section:
Transfer Function