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}

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:

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University