Ana lysis of high-frequency modulation of carrier harmonics for periodically non-stationary random signal - Javorskyj, I.M.; Yuzefovych, R.M.; Lychak, O.V. (Reports of the National Academy of Sciences of Ukraine, 2022)
The covariance and spectral properties of the periodically non-stationary random signals (PNRS), whose carrier harmonics are high-frequency modulated by jointly stationary processes are analyzed. It is shown that the covariance functions of this PNRS and its Hilbert transform are the same and their cross-covariance functions have different signs. The representation of the narrow-band PNRS in the form of a superposition of the stationary, but jointly periodically non-stationary components is obtained. The Hilbert transforms of this representation are analyzed, and the formulae for the Fourier coefficients for the covariance function of an analytic signal are derived. These formulae show their dependences on auto- and cross-covariance functions of the narrow-band component quadratures. It is shown that such quadratures can be extracted and analyzed using the Hilbert transform.