How to detect the cyclostationarity in heavy-tailed distributed signals

Abstract Many real phenomena exhibit non-Gaussian behavior. The non-Gaussianity is mainly manifested by impulsive behavior of the real signals that, typically is not visible in the Gaussian-based models. However, the non-Gaussian signals possess substantial analysis challenges to scientists and statisticians. In this paper, we examine the cyclostationary α − stable time series. The classical definition of the second-order cyclostationary models assumes the periodic behavior of the autocovariance function. However, for the general α − stable models the theoretical autocovariance is not finite, thus there is a need to extend the classical definition to the infinite-variance case. To properly define the cyclostationarity property in the general case, in this paper we propose to apply the autocodifference, as the general measure of interdependence for infinitely divisible models. We also present this measure as the appropriate tool for cyclic behavior identification in the case of the α − stable distribution. This paper is the continuation of the authors’ previous research, where the autocodifference was proposed as the measure of interdependence for continuous-time processes with infinite variance. The motivation of the paper is the condition monitoring area where the cyclic behavior identification of the vibration signal is the classical approach for local damage detection. The vibration signals measured on the machines are non-Gaussian, thus the classical methods for cyclic impulsive behavior recognition are not effective and the new methodology needs to be proposed.