Exploiting features of symmetric polynomials for improved comb filter design

This paper presents a simple method to increase alias rejection in comb decimation filters. The method is based on exploiting the properties of the system function of the convolution of a comb filter with itself. Specifically, we take advantage of the fact that this system function is a symmetric polynomial, with a special relation between its coefficients and the position of its zeros on the unit circle in complex z-plane. By appropriately choosing the centermost coefficient of this polynomial, we can separate the double zeros of the polynomial and thus increase the width of the folding bands of the derived structure. The resulting structure is multiplierless; we contrast it with some existing methods and demonstrate the benefits of the proposed design technique.