New differential coefficient coding algorithm for recursive FIR filters

This paper describes a new efficient resource saving differential coefficient coding algorithm for linear phase recursive FIR filters. Increased resource savings and filter performance are obtained by avoiding the common approach adopted by other methods which rely on recursive accumulator section coefficients derived from the signed or unsigned binomial distribution and minimisation of the error between the recursive FIR filter impulse response and that of the original (non-recursive) prototype. Instead an accumulator transfer function optimisation is carried out to minimise the variance of the differentially encoded coefficients, allowing the original filter performance to be verified a priori and maintained in the conversion to a recursive FIR design. The method ensures no degradation in sample processing rate and affords maximum hardware reduction for both narrow and wide-band filtering functions through use of a new accumulator structure and parallel filter decomposition technique. Two examples demonstrate the effectiveness of the algorithm in comparison with other reported approaches.