The design of specialized residue classes for efficient recursive digital filter realization

The design of residue number system recursive digital filters requires scaling to prevent overflow. This paper presents special residue classes in which scaling is a simple operation that can be easily mechanized. This hierarchy of useful residue classes is described, and quantization error due to residue scaling is analyzed in each class. Computer simulations of a recursive Chebyshev band reject filter are included to illustrate filter performance in these RNS classes.