Figure 2.26 shows a family of feedback-comb-filter
amplitude responses, obtained using a selection of feedback
Amplitude response of the feedback
(Fig.2.24 with and
) with and , , and . a) Linear
amplitude scale. b) Decibel scale.
Figure 2.27 shows a similar family obtained using
negated feedback coefficients; the opposite sign of the feedback
exchanges the peaks and valleys in the amplitude response.
Amplitude response of the phase-inverted feedback comb-filter, i.e., as in Fig.2.26 with negated
, , and .
a) Linear amplitude scale. b) Decibel scale.
As introduced in §2.6.2 above, a class of feedback comb
filters can be defined as any difference equation of the form
Taking the z
transform of both sides and solving for
the transfer function
of the feedback comb filter is found to be
so that the amplitude response is
This is plotted in Fig.2.26
. Figure 2.27
shows the same case but with the feedback
For , the feedback-comb amplitude response
which exactly inverts the amplitude response of the feedforward
Note that produces resonant peaks at
, the peaks occur midway between these values.
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