Efficient variable-coefficient RNS-FIR filters with no restriction on the moduli set

Introduction of residue number systems (RNS) into hardware realization of high dynamic range FIR filters is known to be advantageous. However, deciding on the number and forms of the moduli, and nature of the filter coefficients is a critical issue, wherein all the previous relevant works lean on RNS multiplication schemes that only work with restricted forms of moduli (e.g., only prime numbers) or only constant FIR coefficients; hence considerably tightening the design space. As a remedy, we propose a modulo-(2(n) - delta) multiplier/accumulator scheme (The parameter n represents the bit-width of the corresponding residue channels wherein the other parameter delta determines the exact value of the corresponding modulo) with no restriction on the value of delta (except that delta < 2(n-1), for balancing the widths of residue channel), nor on the constant/variable nature of the coefficients. The key to this liberty of choice is the especial handling of the end-around carries of modular operations that results in performing only regular non-modular operations, except for the last two that yield the final result. Simulation and synthesis of the proposed circuits show speed, cost and power gains.