Elimination of constant-input limit cycles in recursive digital filters using a generalised minimum norm

Abstract

The concept of a minimum norm which is not the Euclidian norm is presented and used to eliminate autonomous limit cycles in recursive digital filters. This concept is then extended to include the elimination of constant-input limit cycles. An implementation of a 2nd-order coupled form filter which is free of limit cycles under all constant-input conditions is presented. The generalised minimum norm N(X(k))2 and the integer equilibrium state X-e of four 2nd-order filters are also compared.