Parallel and Modular Structures for FIR Digital Filters (Special Section on the 6th Karuizawa Workshop on Circuits and Systems)

概要

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The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general, the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and efficient filtering specially for maximally flat transfer functions.
社団法人電子情報通信学会の論文
1994-03-25