Implementation of the generalized FIR filter structure using the residue arithmetic

Very recently, the Quadratic Residue System (QRNS) has been introduced [3,4,5]. Using the QRNS complex multiplication can be performed with two base field multiplication and zero additions. The primary restriction is the limited form of the moduli set for RNS operations. The QRNS has since been geralized for any type of moduli set with an increase in multiplication from 2 to 3 and the resulting number system has been termed Modified Quadratic Residue Number System (MQRNS) [1,2]. In [9] a recursive FIR filter has been developed using the Complex Number Theoretic z-transform (CNT z-transform). Recently, in [6], the implementation of this recursive FIR filter structure has been presented using the QRNS and the MQRNS. Extension of this implementation to generalized FIR filter (Lagrange) has also been briefly presented in [6]. In this paper, we consolidate the implementation aspects of the generalized FIR filter using the MQRNS and also prove that the QRNS is not a suitable medium for the implementation.