Simplified Feedback Comb Filter

Consider the special case $b_0=1$, $-a_M = g \; \Rightarrow$

$$\begin{eqnarray*} y(n) &=& x(n) + g\, y(n-M)\\ H(z) &=& \frac{1}{1-g\,z^{-M}} \end{eqnarray*}$$

• Impulse response is a series of echoes, exponentially decaying and uniformly spaced in time
• Models a plane wave between parallel walls
• Models a displacement wave on a guitar string
• $g$ = round-trip attenuation
  • two wall-to-wall traversals
  • two wall reflections