Simplified Feedback Comb Filter, Cont'd

For a sinewave input and $0<g<1$:

• Gain is maximum [$1/(1-g)$] when a whole number of periods fits in $M$ samples:
  $$\omega_k T = k\frac{2\pi}{M}, \quad k=0,1,2,\dots$$
  These are again the $\hbox{DFT}_M$ basis frequencies

• Gain is minimum [$1/(1+g)$] when an odd number of half-periods fits in $M$ samples:
  $$\omega_k T = (2k+1)\frac{\pi}{M}, \quad k=0,1,2,\dots$$