Efficient residue arithmetic based parallel fixed coefficient FIR filters

This paper presents new structures and results for the implementation of fixed coefficient filters using residue arithmetic and parallel FIR filters. The enhancements obtained are through the application of the residue number system. Parallel FIR filters offer a means of reducing the computational complexity with varying degrees of tradeoffs in the added latency and complexity reduction. The parallel FIR filters in this paper use efficient Mersenne and Fermat number theoretic transforms to obtain the input for the decimated sub filters. Through utilizing a minimum spanning tree algorithm for modulo multiplication, a very low cost transpose multiplier block is obtainable. This is then used for the implementation of the sub filters that form part of the parallel FIR architecture. The combined benefits result in low complexity architectures using residue arithmetic for large fixed coefficient filters.