comb filter

notes from "A Comb Filter Design Using Fractional-Sample Delay" [1]:

• transfer function of the filter: $H_C\left(z\right)=\frac{1-z^{-D}}{1-\rho^D z^{-D}}$, where $D$ is the period of harmonic interference (see block diagram below);
• if $D$ is integer, filter realization is straight forward;
• if $D$ is a fraction, we can use the the techniques in "Splitting the unit delay" [2] to realize $z^{-D}$; FIR frac delay filter or All-Pass frac delay filter;
•  an extra optimization that [1] proposes is to make sure that the filter response has an actual zero at  $w_0=\frac{2\pi}{D}$ frequency;

comb filter to remove periodic interference, where $D$ is the period of the interference harmonic