Criteria for Determining if a High-Order Digital Filter Using Saturation Arithmetic is Free of Overflow Oscillations

Recently1 we made the unexpected observation that, among recursive filters employing saturation arithmetic, a fundamental difference exists between second and higher order filters, namely, the latter may sustain large-amplitude overflow oscillations. This observation proved to be timely since it coincided with the awareness that economies of scale coupled with various recent developments make highly attractive the use of high-order sections in filter realizations. It has also come to light that the problem of possible large-scale oscillations is of interest not only in data filtering but in other areas where the natural structure is a 1679 high-order recursive system, e.g., code converters (DPCM speech synthesizers.