Exploring three classes of symmetrical polynomials for improving comb filter design

Abstract

This paper explores certain classes of symmetrical polynomials, with all zeros on unit circle, to improve frequency characteristic of comb filters, in a stop band. More specifically, three classes of symmetric polynomials with all coefficients equal to 1, with coefficients equal to 0 and 1, and with the coefficients equal to 1 and ¼, respectively, are investigated. All three classes of polynomials have all zeros on the unit circle. This characteristic is important to improve comb alias rejection by properly relating the parameters of the polynomials with the parameters of the corresponding comb filter. The proposed approach is illustrated with one example and compared with the original comb filter.