Ana lysis of high-frequency modulation of carrier harmonics for periodically non-stationary random signal
Keywords:periodically non-stationary random signals, high-frequency modulation, Hilbert transform, quadrature components
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.
Dragan, Ya. & Yavorsky, I. (1980) Rhytmics of Sea Waving and Underwater Acoustic Signals, Kyiv: Naukova Dumka (in Russian).
Gardner, W. A. (1985). Introduction to Random Processes with Applicattions to Signals and Systems, New York: Macmillan.
Dragan, Ya., Yavorskyj, I. & Rozhkov, V. (1987). Methods of probabilistic analysis of oceanological rhytmics, Leningrad: Gidrometeoizdat (in Russian).
Gardner, W. A. (1994). Cyclostationarity in Communications and Signal Processing, New York: IEEE Press.
Hard, H. L. & Miamee, A. (2007). Periodically Correlated Random Sequences: Spectral Theory and Practice, New York: Wiley.
Antoni, J. (2009). Cyclostationarity by examples. Mech. Syst. Signal Process., 23, pp. 987-1036. https: //doi. org/10. 1016/j. ymssp. 2008. 10. 010
Javorskyj, I., Yuzefovych, R., Matsko, I. & Kravets, I. (2015). The stochastic recurrence structure of geophysical phenomena. Applied Condition Monitoring, 3, pp. 55-88. https: //doi. org/10. 1007/987-3-319-163330-7_4
Napolitano, A. (2020). Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations, Elsevier: Academic Press, 2020.
Javorskyj, I. (2013). Mathematical models and analysis of stochastic oscillations, Lviv: Karpenko Physico- Mechanical Institute (in Ukrainian).
Javorskyj, I., Leskow, J., Kravets, I., Isaev, I. & Gajecha-Mizek, E. (2011). Linear filtration methods for statistical analysis of periodically correlated random processes. — Part II: harmonic series reprsentation, Signal Process., 91, pp. 2506-2519. https: //doi. org/10. 1016/j. sigpro. 2011. 04. 031
Mykhailyshyn, V., Javorsky, I., Vasylyna, Ya., Drabych, O. & Isaev, I. (1997). Probabilistic models and sta tistical methods for the analysis of vibrational signals in the problem of diagnostics of machines and structures, Mater. Sci., 33, pp. 655-672.
Begrosian, E. (1963). A product theorem for Hilbert transforms, Proc. of the IEEE, 51, pp. 868-869.
Bendat, J. S. & Piersol, A. G. (2010). Random Data: Analysis and Measurement Procedures, John Wiley and Sons Ltd.
Randall, R. B. & Antoni, J. (2011). Rolling element bearing diagnostics – A tutorial, Mech. Syst. Signal Process., 25, pp. 485-520. https: //doi. org/10. 1016/j. ymssp. 2010. 07. 017
Randall, R. B., Antoni, J. & Chobsaard, S. (2001). The relation between spectral correlation and envelope analysis, Mech. Syst. Signal Process., № 15 (5), pp. 945-962. https: //doi. org/10. 1006/mssp. 2001. 1415
How to Cite
Copyright (c) 2022 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.