Sharpening Minimum-Phase FIR Digital Filters Using Paired Prototypes
Gerald D. Cain, Anush Yardim, Fredric J. Harris · 2020
Digital filter sharpening aims to improve the performance of a prototype filter by cascading it with a “partial compensator” incorporating multiple uses of that same coefficient set. The Kaiser & Hamming sharpening structure has long been the established “standard point of departure” for sharpening FIR filters despite its severe usage restrictions (to only odd-length linear-phase prototypes). Here we achieve greater flexibility by embracing prototype pairs in internal pathways of our recently introduced sharpener. By the simple additional expedient of conjugate-reversal of designated coefficient vectors we then force a linear-phase condition which eradicates internal delay alignment trouble. This combination permits prototypes of any phase type or length to undergo sharpening, and allows either linear, mixed, or minimum-phase results to be delivered. Performance of two new alternative structures is highlighted here in one complex and several real filter sharpening examples, with primary targeting of the important class of minimum-phase filters.