Fast Averaged Cyclic Periodogram method to compute spectral correlation and coherence

Cyclostationary signal analysis is increasingly adopted in many fields such as communications, meteorology, vibration analysis, and others. Spectral correlation and spectral coherence are two powerful tools that can be applied to detect cyclostationarities in the signal even when the useful information is concealed by a strong random noise. In this paper, a fast method is proposed to calculate the Averaged Cyclic Periodogram (ACP), which is widely applied in many fields and due to its robustness as an estimator of spectral correlation and coherence. The method calculates shifted transforms for part of the cyclic frequency range and utilizes the frequency shifting property of Fourier transform to extract the spectral correlation/coherence for the entire frequency range. The proposed method is proved to save considerable time in comparison to the normal ACP method and the fast spectral correlation method which was proposed by some scholars. The proposed method does not require large memory, making it suitable for low-memory platforms. The application examples using simulated and actual vibration signals have demonstrated the accuracy of the method and its applicability to analyze cyclostationary signals where the cyclic event interval is constant and also cyclo-non-stationary signals where the cyclic event interval is variable.