Digital filter realizations without overflow oscillations

Abstract

Most of the literature dealing with overflow oscillation in fixed-point arithmetic digital filters has considered the direct form exclusively. It is possible to eliminate overflow oscillations, regardless of pole locations, by considering more general forms. A sufficient condition is given for a two's complement state variable realization of any order to be free of overflow oscillation. A simple characterization of the condition is given for second-order filters. Among those second-order forms which meet the condition are normal forms, and forms which minimize output roundoff noise.