Scaling Function Based on Chinese Remainder Theorem Applied to a Recursive Filter Design

Abstract

Implementation of IIR filters in residue number system (RNS) architecture is more complex in comparison to FIR filters, due to introduction of the scaling function. This function performs operation of division by a constant factor, which is usually the power of two, and after that the operation of rounding. In that way dynamic range reduction in digital systems is achieved. There are different methods for scaling operation implementation, already presented in references. In this paper, some RNS dynamic reduction techniques have been analyzed and then application of one selected technique has been presented on example. In all RNS calculations the power of two moduli set {2ⁿ –1, 2ⁿ , 2ⁿ +1} has been applied.