General criterion for the absence of limit cycles in filter structures with a single quantizer

A criterion for the absence of zero-input limit cycles in recursive digital filter structures that can be implemented with a single quantizer in the recursive loop is presented. The criterion can be applied with a rounding or with a magnitude truncation quantizer and accounts for the use of error feedback as well. Additionally, a criterion for the elimination of constant-input limit cycles is formulated. The criteria are applied to several well-known filter structures. Since most of the structures have previously been analyzed in a multiquantizer implementation only, new results on their stability properties in the single-quantizer configuration are obtained