Reformulation of Chang´s criterion for the absence of limit cycles using bilinear transform

A procedure for the reformulation of Chang´s criterion (1981) for the absence of zero-input limit cycles in recursive digital filters is presented. The technique employs the standard bilinear transform to convert a frequency-domain criterion into a polynomial form in terms of matrix transformations. The use of the method is illustrated with design examples applied to determine the stability region for certain single-quantizer recursive filter structures. The results can be utilized, e.g., in the design of an error feedback network for a given filter such that limit cycles are eliminated