Digital filter realizations without overflow oscillations

Most of the literature dealing with overflow oscillations in fixed-point digital filters has considered the direct form realization exclusively. In direct forms the question of whether oscillations are possible depends on the location of the poles of the filter. We show that it is possible to eliminate overflow oscillations, regardless of pole locations, by considering more general realizations. A sufficient condition is given for a state variable realization (using two's complement arithmetic) of any order to be free of overflow oscillation. A simple characterization of this condition is given for second order filters. Among second order realizations which meet the condition are so-called normal realizations and structures which minimize roundoff noise.