Stability of normal form digital filters with two´s complement quantization

Normal-form digital filters are investigated for limit cycles due to two´s complement truncation quantization. Regions in the parameter plane of a coupled-form filter are obtained where various types of period-one limit cycles are possible. A sufficient condition is established for the global asymptotic stability of a quantized coupled-form digital filter. A bound on the amplitude of limit cycles is obtained. This is used to develop an algorithm to check whether or not limit cycles are possible in a given filter. If possible, the algorithm produces all the initial conditions and periods for all possible limit cycles