New resource saving differential coefficient coding algorithm for recursive FIR filter design

Description/Abstract

Differential coefficient coding converts a non-recursive FIR filter into a recursive filter with the aim of reducing both maximum and average coefficient magnitudes. This paper describes a new efficient resource saving differential coefficient coding algorithm for linear phase FIR filters. The savings are obtained by not restricting the recursive section coefficients to variations of the binomial distribution as with previous approaches suitable only for narrow-band filters. Instead, an optimisation is carried out to minimise the variance of the encoded coefficients affording maximum hardware reduction for both narrow and wide-band filtering functions. Implementation of recursive FIR filters produced by the algorithm requires use of parallel filter decomposition and feedthrough accumulator structures which are both described in deatil. When compared with previous approaches, resource savings of over 40% are demonstrated.