Hilbert transform of periodically non-stationary random signals: narrow-band high frequency amplitude modulation

Using Hilbert transform for the analysis of periodically non-stationary random signals (PNRS), is discus-sed. The narrow-band high frequency amplitude modulation is considered. It is shown that, the auto-covariance functions of a signal and its Hilbert transform are the same and its cross-covariance functions differ only by a sign, which results in an identity of cyclic spectrums of variances for analytic and raw signals. It is shown that band-pass filtering can reduces both the number of signal variance cyclic harmonics and their amplitudes.