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In this paper, the design of a Finite Impulse Response (FIR) filter based on   the residue number system (RNS) is presented. We chose to implement it in the   (RNS), because the RNS offers high speed and low power dissipation. This   architecture is based on the single RNS multiplier-accumulator (MAC) unit.   The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to   design FIR filter. A numerical example illustrates the principles of residue   encoding, residue arithmetic, and residue decoding for FIR filters

Constant-coefficient FIR filters based on residue number system arithmetic