Feedforward Comb Filters

Comb filters get their name from the shape of their magnitude response and are important components of audio signal processing networks. It turns out that the acoustic echo model developed earlier is one instance of a feedforward comb filter.

• A feedforward comb filter is illustrated in Fig. 19.

  Figure 19: A feedforward comb filter block diagram.

  

  The difference equation for this filter is given by:

  $$y[n] = b_{0}x[n] + b_{M}x[n-M].$$

• The feedforward comb filter is equivalent to the echo simulator of Fig. 18 if $b_{0} = 1$ and $b_{M} = g$. In this way, the feedforward comb filter is a computational physical model of a single discrete echo.

• The magnitude response of a feedforward comb filter is shown in Fig. 20 for $M = 5$, $b_{0} = 1$, and $b_{M}$ = 0.1, 0.5, and 0.9.

  Figure 20: Magnitude response of a feedforward comb filter with $M = 5$, $b_{0} = 1$, and $b_{M}$ = 0.1, 0.5, and 0.9.

  

• The following MSP patch implements a feedforward comb filter.