Limit cycles in large moduli residue number system digital filters

The large moduli residue number system (RNS), defined by the three moduli set
(2^{n} - 1,2^{n}, 2^{n} + 1}
, has recently been shown to possess several attractive properties. In particular,.amplitude scaling is a much simplified operation through the use of the autoscale algorithm. The error introduced by the scaling algorithm is the counterpart of the roundoff error found in fixed-point arithmetic. This error can cause limit cycling in large moduli RNS digital filters. Necessary conditions for the existence of period-one and -two limit cycles are derived and the principal differences between the limit cycles in fixed-point and RNS filters are discussed.