A state-space approach for elimination of limit cycles in digital filters with arbitrary structures

A directed graph is introduced to treat state transition of digital filters with arbitrary structures. State space of the digital filter defined as a finite subset of lattice group is divided into four subsets from a point of view of the state transition about the limit cycles including overflow oscillations. Based on the concept of the four subsets proposed here, the state distribution is obtained by the aid of a computer. Two algorithms are presented to eliminate the limit cycles of any digital filters using the state distribution computed. An example is represented to show how the algorithms are applied for the elimination of the limit cycles.