Computation of harmonic comb filter weights

Harmonic comb filters are characterized in the frequency domain by notches arranged at equal intervals, and centered about DC. For a finite impulse response harmonic comb filter, the characteristic polynomial has its roots on the unit circle at equal angular intervals, symmetrically about 1+j0. A simple formula for the coefficients of such a polynomial and for their derivatives with respect to the frequency interval is presented. This result is applied as well to the computation of Butterworth filter parameters