Feed-Forward Comb-Filter Amplitude Response

Recall:

• Linear (top) and decibel (bottom) amplitude scales
• $H(z) = 1 + g z^{-M}$
  • $M=5$
  • $g=0.1, 0.5, 0.9$
• $G(\omega)\mathrel{\stackrel{\mathrm{\Delta}}{=}}\left\vert H(e^{j\omega T})\right\vert = \left\vert 1 + g e^{-jM\omega T}\right\vert \to 2\cos(M\omega T/2)$ when $g=1$
• In flangers, these nulls slowly move with time

For $g>0$, there are $M$ peaks in the frequency response, centered about frequencies

$$\omega^{(p)}_k = k \frac{2\pi}{M}, \quad k=0,1,2,\dots,M-1.$$

For $g=1$ (maximum ``flanging depth''), the peaks are maximally pronounced, with $M$ notches occurring between them at frequencies $\omega^{(n)}_k = \omega^{(p)}_k + \pi/M$.

Notch spacing is inversely proportional to delay-line length