Complex digital signal processing using quadratic residue number systems

Recently, the Quadratic Residue Number System (QRNS) has been introduced [4,5,6], which allows the multiplication of complex integers with two real multiplications. Restrictions on the form of the moduli can be removed if an increase in real multiplications from two to three can be tolerated; the resulting number system has been termed the Modified Quadratic Residue Number System (MQRNS). In this paper the MQRNS is defined, and residue to binary conversion techniques in both the QRNS and MQRNS are presented. Hardware implementations of non-recursive and recursive digital filters are also presented where the QRNS and MQRNS structures are realized using a bit-slice architectures.