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:
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