Hilbert Transform for Analysis of Amplitude Modulated Wide-band Random Signals

Hilbert transform of the wide-band high frequency amplitude modulation is considered. It is shown that its covariance function is the same as covariance function of the raw signal and cross-covariance functions of them differ only by a sign. It results in an identity of cyclic spectrums of variances for analytic and raw signals. The properties of band-pass filtered signals are examined and it is shown that band-pass filtering can reduce both the number of signal variance cyclic harmonics and their amplitudes. Relationships linking the covariance components of analytical signals and auto-covariance and cross-covariance functions of their quadratures are ascertained.