Generalized spectral coherence for cyclostationary signals with α-stable distribution

摘要

The statistical characteristics of cyclostationary signals vary periodically in time. In the Gaussian (or second-order) case this property is typically related to the periodic autoco-variance function. Thus, many classical methods for detection of cyclostationarity are based on the analysis of autocovariance in time and frequency domain. In the frequency analysis, one of the most powerful tool is the spectral coherence. However, many real signals exhibit behavior adequate to non-Gaussian behavior. This is mostly related to the impulsiveness of the signals. In that case, the usage of the heavy-tailed distribution is a more appropriate. We propose to consider a-stable distribution which seems to be perfect for the impulsive behavior modeling. In this paper, the a-stable cyclostationary signals are examined and the generalization of the classical spectral coherence is proposed. The new bi-frequency map is based on the autocovariation function, which is defined for a-stable signals. It is demonstrated that the proposed statistic is not influenced by the large observations contained in the signal and thus it is more appropriate for the considered case. The introduced approach is validated for the simulated signal and for the real vibration signal from the rolling element bearings operating in crushing machine.