Ana lysis of high-frequency modulation of carrier harmonics for periodically non-stationary random signal
DOI:
https://doi.org/10.15407/dopovidi2022.02.021Keywords:
periodically non-stationary random signals, high-frequency modulation, Hilbert transform, quadrature componentsAbstract
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.
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