A computer-aided test for the characterization of parasitic oscillations in IIR digital filters

In this paper, an algorithm that can be utilized to determine the behaviour of limit cycles in a fixed-point digital filter is given. Also, this paper presents the formulation used to describe the filters in order to evaluate any actual realization, order, type of quantization and the precision of the accumulator. Actual bounds on the amplitude, period and output of limit cycles are developed. It is based on experimental results showing that all states in limit cycles are confined in a closed region, where the proposed algorithm makes a study in depth. It is oriented to be used in a processor and characterizes the impact of limit cycles in significantly less time than other formulations. The good performance of the algorithm is summarized in a table that compares the results with classical exhaustive formulations and other theoretical calculations.