On the Nyquist frequency of random sampled signals

In modern industry, the wide use of reliable and sophisticated sensors with their connection to internet has introduced the phenomena of Big Data, especially in the field of condition monitoring systems (CMSs) in e-maintenance applications. In particular, in the case of vibration signals, high-performance acquisition systems are required, characterized by anti-aliasing filtering and high uniform sampling rate, in order to properly digitalize the meaningful frequency content of the signals. In this context, the capability of non-uniform random sampling (RS) is assessed in this work. While in different fields, such astronomy, structural and biomedical studies, the RS is a problem to be resolved, due to the unavailability of samples at specific instants (missing data problem), in the field of fault detection & diagnosis (FDD), RS can be a chosen sampling method thanks to its advantages: Anti-aliasing property and low average sampling rate. Therefore, this paper focuses on studying the anti-aliasing property of the random sampled data, verifying the criterion proposed in literature for establish the Nyquist frequency, and analyzing its sensitivity to the sampling parameters. This study is carried out using simulated signals and computing the spectral window, giving the Nyquist frequency for different random sampling parameters; moreover, a spectral analysis method, the Schuster periodogram, is used to verify when the spectrum is actually free of alias. The results show that the Nyquist frequency depends on the numerical accuracy of the randomly generated time instants.