Feedback Comb Filters

• A feedback comb filter is illustrated in Fig. 9.

  Figure 9: A feedback comb filter block diagram.

  

  The difference equation for this filter is given by:

  $$y[n] = b_{0}x[n] - a_{M}y[n-M].$$
  For stability, the coefficient $\vert a_{M}\vert \leq 1$.

• The feedback comb filter can be regarded as a computational physical model of a series of echoes, exponentially decaying and uniformly spaced in time.

• The impulse response of a feedback comb filter for $M = 5$, $b_{0} = 1$, and $a_{M}$ = 0.6 is shown in Fig. 10.

  Figure 10: Impulse response of a feedback comb filter with $M = 5$, $b_{0} = 1$, and $b_{M}$ = 0.6.

  

• The magnitude response of a feedback comb filter is shown in Fig. 11 for $M = 5$, $b_{0} = 1$, and $a_{M}$ = -0.1, -0.5, and -0.9.

  Figure 11: Magnitude response of a feedback comb filter with $M = 5$, $b_{0} = 1$, and $a_{M}$ = -0.1, -0.5, and -0.9.

  

• The following Pd patch implements a feedback comb filter (note there is a 1 ms delay minimum using the delread~ object).
  

• The comb~ object in Pd implements a combined feedback/feedforward comb filter with inputs for various parameters (delay time and coefficients).