Feedforward Comb Filters

Comb filters get their name from the shape of their magnitude response and are important components of audio signal processing networks.

• A feedforward comb filter is illustrated in Fig. 10.

  Figure 10: 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 transfer function of the feedforward comb filter is
  $$H(z) = b_{0} + b_{M} z^{-M},$$
  from which the amplitude response is found as
  $$G(\omega) \ensuremath{\stackrel{\Delta}{=}}\left\vert H(e^{j \ome... ... + b_{M} e^{-j \omega M}\right\vert, \hspace{0.2in} -\pi \leq \omega \leq \pi.$$

• The magnitude response of a feedforward comb filter, calculated with the Matlab script combs.m, is shown in Fig. 11 for $M = 5$, $b_{0} = 1$, and $b_{M}$ = 0.1, 0.5, and 0.9.

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