Design of multiplier-less minimum-phase filters based on sharpening compensated comb filters

Abstract

Minimum-phase (MP) filters have all zeros inside and/or unit circle. As a consequence, the group delay of an MP system is always less than that of non-minimum phase systems, having the equal magnitude responses. Minimum-phase (MP) filters find applications where it is necessary to have a low group delay, like in communications, speech processing, and predictive coding, among others. This paper presents a novel simple method for the direct design of low-pass minimum-phase (MP) filters. Method is based on design of two compensated combs, using a multiplier-less minimum-phase compensator, and sharpening technique. The first comb defines the stop band and pass band of the MP filter, while the second comb decreases side lobes of the first comb, thus increasing attenuation of the resulting MP filter. Knowing that all zeros of comb filter are on the unit circle, the compensated comb is also a MP filter. Similarly, under the special condition, the sharpening of multiplier-less compensated comb may also result in a MP multiplier-less filter. The benefit of the proposed method is illustrated in the provided design examples.