Elimination of zero-input and constant-input limit cycles in single-quantizer recursive filter structures

A general criterion for the absence of zero-input limit cycles in digital filter structures that can be implemented with a single quantizer in the recursive loop is presented. The criterion can be applied to a rounding or magnitude truncation quantizer, and it allows the use of error feedback as well. Additionally, a method for the elimination of constant-input limit cycles is presented, provided that the implementation is already free from zero-input limit cycles. The criteria are applied to several well-known filter structures, and new results on their limit cycle properties in the single-quantizer configuration are obtained. It is shown that certain structures are always free from all zero-input and constant-input limit cycles when magnitude truncation is used for quantization. The single-quantizer structures can always be provided with appropriate error feedback, not only to achieve the elimination of limit cycles but also to reduce the roundoff noise, resulting in excellent overall performance