Recent Advances in Residue Number Techniques for Recursive Digital Filtering

A new algorithm for scaling in residue number systems (RNS's) is presented for applying residue number theory to recursive digital filtering. The algorithm provides an efficient method for scaling the output of each recursive filter section for use in subsequent iterations of the recursion. Four classes of residue systems are described in which scaling is simple and quantization errors are minimized, thereby combining good quantization error performance with the advantages of high-speed residue arithmetic. A computer analysis of the scaling quantization errors is presented, as well as some results from a recursive residue simulation. Three hardware architectures are described for the realization of recursive residue filters.