Fast RNS DSP algorithms implemented with binary arithmetic

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Fast RNS (residue number system) algorithms which use only binary arithmetic are developed. Scaled residues, called pseudoresidues, are introduced by exploiting the cycle properties of each RNS channel and solving a Diophantine equation. Using the pseudoresidues instead of the original residue set to perform the desired computations, an RNS processor can be built with standard binary devices of small wordlength. The effectiveness of the procedure is shown by developing the pseudoresidue implementations of a modular multiplier for odd moduli RNS and of a FIR (finite impulse response) filter. The resulting structures exhibit complete reprogrammability for both moduli and coefficients, a very low number of fast machine cycles, and a square time-area product reduction. >