Composite Sharpening of FIR Digital Filters

The effectiveness of the popular Kaiser & Hamming sharpening structure is severely limited, not suitable for use outside the class of FIR filters with symmetric impulse responses. We introduce a functional composition framework which removes this barrier by adopting a two-level sharpening regimen that exploits “multiple sharpening passes” whenever single-instance sharpening proves inadequate. The “primary” stage uses a conjugate-reversal twin-prototype sharpener. We exhibit and exercise two such recently-introduced structures of the required sort in this paper. One key feature is their optional delivery of linear-phase sharpened resultants. This provides handover for “secondary” sharpening, liberating otherwise ineffectual sharpening structures to then contribute. In this way, provision of extra multistage sharpening potency treats the whole original sharpener to a cumulative re-sharpening, rather than the counter-productive approach of simply cascading isolated fixed sharpener instances. The composite processing uses “nesting” as a worthwhile and practical alternative to ever-larger singlesharpener units. Several examples illustrate the method.