Abstract

Periodically correlated random processes (PCRP, also known as Cyclostationary or periodically non-stationary) is an adequate model for describing the physical phenomena, where stochasticity and recurrence play significant role. The PCRP properties, in Gaussian assumption, can be described by first- and second-order probabilistic characteristics – the mean, correlation function and spectral density. Estimating operators for these characteristics (as well as for any other kind of non-stationarity) should be deduced taking into account their time variability, finite record length, and possibility to estimate the signal characteristics for unit record (so called ergodicity problem). The coherent method, which is based on averaging the signal values via correlation period, and the component method, which is based on the Fourier transform will be shown. Comparision between the coherent and component estimates will be carried out. Also, I focus attention on the methods for hidden periodicity search. An important part for understanding the PCRP structure is the PCRP decomposition into stationary connected random processes (harmonic serial representation). Provided the specific form for the harmonic components, we can construct the additive, multiplicative, poly-harmonic models, etc. Based on this, we develop the new algorithm for PCRP decomposition and the new approach for PCRP parametrical modelling. The practical usage of PCRP methods will be shown for vibro-acoustic and music examples.