### Feedback Comb FilterAmplitude Response

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

 (3.5)

so that the amplitude response is

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.

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Feedforward Comb Filter Amplitude Response