Information and Diagnostics Systems
Hilbert Transform of Biperiodically Non-Stationary Random Signals
Keywords
biperiodically non-stationary random process, Hilbert transform, covariance and spectral components, analytic signal
Abstract
An analysis of the covariance and spectral structure of the Hilbert transform of biperiodically non-stationary random processes, which are a model of signals with double rhythmicity, are analyzed here. The obtained relations join the cross-covariance and cross-spectral characteristics of the signal and its Hilbert transform with the characteristics of the signal itself.
References
- Javorskyj I.M. Mathematical models and analysis of stochastic oscillations // Lviv, IPM NAS of Ukraine. – 2013. – P 802. (in Ukrainian)
- Napolitano A. Cyclostationary processes and time Series: Theory, applications, and generalizations. Academic Press // Elsevier, London (2020). https://doi.org/10.1016/C2017-0-04240-4
- Javorskyj I., Yuzefovych R., Kravets I., Matsko I. Methods of periodically correlated random processes and their generalizations. In: Cyclostationarity: Theory and Methods. Lecture Notes in Mechanical Engineering. New York // Springer. – 2014. – P.73–93. https://doi.org/10.1007/978-3-319-04187-2_6
- Javorskyj I., Yuzefovych R., Kravets I., Matsko I. Periodically correlated processes: applications in early diagnostics of mechanical systems // Mech. Syst. Signal Process. – 2017. – 83. –:P.406–438. https://doi.org/10.1016/j.ymssp.2016.06.022
- Javorskyj I., Yuzefovych R., Lychak O., Semenov P., Shyepko R. Detection of distributed and localized faults in rotating machines using periodically non-stationary covariance analysis of vibrations // Meas. Sci. Technol. – 2023. – 34. – P.065–102. https://doi.org/10.1088/1361-6501/acbc93
- Javorskyj I., Yuzefovych R., Lychak O., Trokhym G., Varyvoda M. Methods of periodically non-stationary random processes for vibrations monitoring of rolling bearing with damaged outer race // Digit. Signal Process. – 2024. – 145. – № https://doi.org/10.1016/j.dsp.2023.104343