ISSN 0474-8662. Information Extraction and Processing. 2017. Issue 45 (121)
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LSM-harmonic analysis of bi-periodic nonstationary vibration signals

Javorskyj I. M.
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv
Telecommunication Institute of University of Technology and Life Science, Bydgoszcz, Poland
Yuzefovych R. M.
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv
Lviv Polytechnic National University
Dzeryn O. Y.
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv

https://doi.org/

Keywords: bi-periodic nonstationary vibration signal, least squares method, estimators of deterministic part parameters, unbiasedness, and consistency

Cite as: Javorskyj I. M., Yuzefovych R. M., Dzeryn O. Y. LSM-harmonic analysis of bi-periodic nonstationary vibration signals. Information Extraction and Processing. 2017, 45(121), 14-25. DOI:https://doi.org/.


Abstract

The estimators of parameters of bi-periodic nonstationary vibration signal deterministic part, obtained with using the least squares method (LSM), are analyzed. LSM estimation allows avoiding aliasing effects. The formulas for estimators of variance and bias, which describe their dependences on realization length and signal covariance components, are derived. The results are specified for the quadrature model of the signal. LSM has shown its efficiency for separation of harmonics with close frequencies, so it should be considered as the main method for vibration signals analysis. It is shown that its usage allows one to obtain unbiased estimators of bi-periodic nonstationary vibration signal deterministic part regardless of realization length and harmonic frequencies.


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