Figure 2.26 shows a family of feedback-comb-filter amplitude responses, obtained using a selection of feedback coefficients.
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.
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
This is plotted in Fig.2.26 for and , , and . Figure 2.27 shows the same case but with the feedback sign-inverted.
For , the feedback-comb amplitude response reduces to
and for to
which exactly inverts the amplitude response of the feedforward comb filter with gain (Eq. (2.4)).
Note that produces resonant peaks at
while for , the peaks occur midway between these values.