Cyclic Point Processes with Limited Aftereffect for a Pulse Signal Analysis with Significant Pulse Rhythm Variability

摘要

In this paper, we present the results of applying the model of cyclic point processes with a limited aftereffect for the analysis of the rhythmic characteristics of pulsed signals. Being a generalization of recurrent and alternating point processes, we show that cyclic processes can describe event flows with more than two states. The latter circumstance significantly expands the scope of their application, in particular, to biomedical signals. Here, a complete (local) statistical description of the cyclic processes is derived, the asymptotics of their behavior are studied, and a simplified statistical description for the case of stationary modes is given. In the latter case, analytical expressions for the average and second mixed moments of the cyclic process are obtained based on the local statistics. In the most important particular case, the dependence of the features of their structure on the time scales of the signal dynamics and on the ratios between the scales was clarified.