The covariance analysis of the periodically non-stationary random signal with narrow-band modulation of carrier harmonics

The periodically non-stationary random signals (PNRSs), whose carrier harmonics are mo-dulated by jointly stationary high-frequency random processes are analyzed. A representation of the signal in the form of a superposition of high-frequency components is obtained and it is shown that these components are jointly periodically non-stationary random processes. The random process is periodically non-stationary of the second order only in the case when some of the cross-covariance functions of its modulation processes are not equal to zero. The correlations of the PNRP spectral harmonics and the correlations of the modulating processes in series representation are equivalent. Evaluating the specific features of the auto- and cross-covariances for modulating processes as well as contribution of each pair to the covariance component values allows us to detect defects at early stages.