On the Stability of Higher Order Digital Filters Which Use Saturation Arithmetic

On the Stability of Higher Order Digital Filters Which Use Saturation Arithmetic By J. E. MAZO (Manuscript received July 15, 1977) The device of using "saturation arithmetic" to cope with adder overflow in recursive digital filters has, for a number of years now, been known to yield stable operation when the filter is of second order and is linearly stable. Mitra has recently given examples to show that this happy situation does not prevail for higher order filters. Here we investigate conditions on the filter coefficients which would guarantee stability for higher order filters using saturation arithmetic. We are only able to give sufficient conditions for stability. These conditions in their simplest form can be written as linear inequalities involving the coefficients of the filter.