Abstract
The properties of the quadrature components of the narrowband periodically non-stationary random signals (PNRS) determined by using their Hilbert transform are considered. It is shown that the analytic signal is a stationary random process, the covariance function of which is complex-valued, and its real and imaginary parts are connected by Hilbert transform. The formulae describing the dependencies of auto- and cross-covariance functions of the quadratures on the covariance components of the signal are obtained. The relationships between the power spectral densities of the quadratures and their cross-spectral density and the zeroth and the second spectral components of narrowband signal are derived. The obtained results are compared with a stationary case. The investigations of the dependency of the properties for separated-by-Hilbert-transform components on the rate of the covariance vanishing on the bases of the simulated realizations are curried out. It is shown that the analytic signal becomes a periodically non-stationary random process as the vanishing rate increases.
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Javorskyj, I., Yuzefovych, R., Kurapov, P., Lychak, O. (2021). The Quadrature Components of Narrowband Periodically Non-stationary Random Signals. In: Shakhovska, N., Medykovskyy, M.O. (eds) Advances in Intelligent Systems and Computing V. CSIT 2020. Advances in Intelligent Systems and Computing, vol 1293. Springer, Cham. https://doi.org/10.1007/978-3-030-63270-0_48
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