A computer-aided method to obtain the actual maximum amplitude for limit cycles in recursive digital filters
Manuel Utrilla-Manso, Francisco López-Ferreras, Ricardo Mallol-Poyato, Roberto J. López-Sastre, J. Sánchez-Golmayo, Roberto Jiménez-Martı́nez · International Conference on Signal Processing · 2006
In this paper we present an alternative to exhaustive search algorithms for calculating the maximum amplitude of limit cycles in fixed-point digital filters. This algorithm allows us to obtain results quite similar to the corresponding exhaustive procedures but taken significantly shorter time of computing. This important improvement is obtained due to the normal behavior of high stability filters, that present all limit cycles in a confined area. The aim is to get this area as soon as possible since all limit cycles are placed there. The good performance of the algorithm is summarized in two different tables that compare the results with classical exhaustive formulations and other early algorithms. They are obtained after analyzing several filters corresponding to different structures, various approximation functions and under different quantizations conditions. This variety shows the general-purpose character of the algorithm.