Asymptotical separation of harmonics by Singular Spectrum Analysis
DOI:
https://doi.org/10.21638/spbu01.2023.409Abstract
The paper is devoted to the sufficient conditions for the asymptotical separation of distinct terms in the linear combination of harmonics by Singular Spectrum Analysis (briefly SSA).
Keywords:
signal processing, singular spectral analysis, linear combination of harmonics, separability of harmonics, asymptotical analysis
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References
Литература
1. Golyandina N., Nekrutkin V., Zhigljavsky A. Analysis of Time Series Structure. SSA and Related Techniques. Champan & Hall/CRC, Boca Raton, London, New York, Washington D. C. (2001).
2. Nekrutkin V. Perturbation expansions of signal subspaces for long signals. Statistics and Its Interface 3, 297-319 (2010).
3. Kato T. Perturbation theory for linear operators. Berlin, Heidelberg, New York, Springer-Verlag (1995).
4. Golyandina N., Zhigljavsky A. Singular Spectrum Analysis for Time Series, 2nd ed., Springer Briefs in Statistics, Springer (2020).
5. Nekrutkin V., Vasilinetc I. Asymptotic extraction of common signal subspaces from perturbed signals. Statistics and its Interface. 10, 27-32 (2017).
6. Ivanova E., Nekrutkin V. Two asymptotic approaches for the exponential signal and harmonic noise in Singular Spectrum Analysis. Statistics and its Interface 12, 49-59 (2019).
7. Golub G. H., Van Loan Ch. F. Matrix computations, 4th ed. Johns Hopkins University Press. (2013).
8. Zenkova N. V., Nekrutkin V. V. On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis. Vestnik St. Petersburg University, Mathematics 55 (2), 166-173 (2022).
9. Nekrutkin V. V. Remark on the Accuracy of Recurrent Forecasting in Singular Spectrum Analysis. Vestnik St. Petersburg University, Mathematics 56, 1, 35-45 (2023).
References
1. Golyandina N., Nekrutkin V., Zhigljavsky A. Analysis of Time Series Structure. SSA and Related Techniques. Champan & Hall/CRC, Boca Raton, London, New York, Washington D. C. (2001).
2. Nekrutkin V. Perturbation expansions of signal subspaces for long signals. Statistics and Its Interface 3, 297-319 (2010).
3. Kato T. Perturbation theory for linear operators. Berlin, Heidelberg, New York, Springer-Verlag (1995).
4. Golyandina N., Zhigljavsky A. Singular Spectrum Analysis for Time Series, 2nd ed., Springer Briefs in Statistics, Springer (2020).
5. Nekrutkin V., Vasilinetc I. Asymptotic extraction of common signal subspaces from perturbed signals. Statistics and its Interface. 10, 27-32 (2017).
6. Ivanova E., Nekrutkin V. Two asymptotic approaches for the exponential signal and harmonic noise in Singular Spectrum Analysis. Statistics and its Interface 12, 49-59 (2019).
7. Golub G.H., Van Loan Ch. F. Matrix computations, 4th ed. Johns Hopkins University Press. (2013).
8. Zenkova N.V., Nekrutkin V.V. On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis. Vestnik St. Petersburg University, Mathematics 55 (2), 166-173 (2022).
9. Nekrutkin V.V. Remark on the Accuracy of Recurrent Forecasting in Singular Spectrum Analysis. Vestnik St. Petersburg University, Mathematics 56, 1, 35-45 (2023).
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Published
2023-12-23
How to Cite
Nekrutkin, V. V. (2023). Asymptotical separation of harmonics by Singular Spectrum Analysis. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(4), 720–735. https://doi.org/10.21638/spbu01.2023.409
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
