Hilbert Transform of biperiodically nonstationary random signals

An analysis of the covariance and spectral structure of the Hilbert transform of biperiodically nonstationary random processes, which model signals with double rhythmicity, is presented here. The obtained relations connect the cross-covariance and cross-spectral characteristics of the signal and its Hilbert transform with the characteristics of the signal itself. We examine the properties of the analytic signal and present characteristic special cases determined by the spectral features of carrier-harmonic modulation.