Time-Angle Periodically Correlated Processes

Cyclostationary processes have now become an essential mathematical representation of vibration and acoustical signals produced by rotating machines. However, to be applicable the approach requires the rotational speed of the machine to be constant, which imposes a limit to several applications. The object of this chapter is to introduce a new class of processes, coined time-angle periodically correlated, which extends second-order cyclostationary processes to varying regimes. Such processes are fully characterized by a time-angle autocorrelation function and its double Fourier transform, the frequency-order spectral correlation. The estimation of the latter quantity is briefly discussed and demonstrated on a real-world vibration signal captured during a run-up.