A computer-aided test for the absence of limit cycles in fixed-point digital filters

The problem of determining the existence of limit cycles in direct form digital filters with quantization nonlinearities is considered. A method based on an exhaustive search is introduced. It is applicable to all direct form digital filters regardless of the type of quantization arithmetic, the number of quantizers, and the order of the filter. The equivalence between the concept of global asymptotic stability and the exclusion of limit cycles is proved for linearly stable finite-wordlength digital filters. The robustness of this test with respect to coefficient perturbation in the digital filter is presented. The computational aspects of the algorithm are also discussed. The algorithm is shown to be capable of always determining the global asymptotic stability of the tested realization