Abstract
In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design parameters K, L, M. In certain cases (their “Region I”), Selesnick and Burrus were able to derive solutions using only linear algebra; for the remaining cases (“Region II”), they proposed using Gröbner bases. This paper introduces a different method, based on multipolynomial resultants, for analyzing and solving the Selesnick–Burrus design equations. The results of calculations are presented, and some patterns concerning the number of solutions as a function of the design parameters are proved.
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