Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis. / Зенкова, Наталья Валентиновна; Некруткин, Владимир Викторович.
в: Vestnik St. Petersburg University: Mathematics, Том 55, № 2, 01.06.2022, стр. 166-173.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis
AU - Зенкова, Наталья Валентиновна
AU - Некруткин, Владимир Викторович
N1 - Publisher Copyright: © 2022, Pleiades Publishing, Ltd.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - The general theoretical approach to the asymptotic extraction of the signal series from theadditively perturbed signal with the help of singular spectrum analysis (SSA) was already outlined in Nekrutkin (2010, Stat. Its Interface 3, 297–319). In this paper, the example of such an analysis applied to the linear signal and the additive sinusoidal noise is considered. It is proven that, in this case, the so-called reconstruction errors ri(N) of SSA uniformly tend to zero as the series length N tends to infinity. More precisely, we demonstrate that maxi |ri(N)| = O(N−1) as N → ∞ if the “window length” L equals (N + 1)/2. It is important to mention that a completely different result is valid for the increasing exponential signal and the same noise. As is proven in Ivanova and Nekrutkin (2019, Stat. Its Interface 12(1), 49–59), no finite number of last terms of the error series tends to any finite or infinite values in this case.Keywords:
AB - The general theoretical approach to the asymptotic extraction of the signal series from theadditively perturbed signal with the help of singular spectrum analysis (SSA) was already outlined in Nekrutkin (2010, Stat. Its Interface 3, 297–319). In this paper, the example of such an analysis applied to the linear signal and the additive sinusoidal noise is considered. It is proven that, in this case, the so-called reconstruction errors ri(N) of SSA uniformly tend to zero as the series length N tends to infinity. More precisely, we demonstrate that maxi |ri(N)| = O(N−1) as N → ∞ if the “window length” L equals (N + 1)/2. It is important to mention that a completely different result is valid for the increasing exponential signal and the same noise. As is proven in Ivanova and Nekrutkin (2019, Stat. Its Interface 12(1), 49–59), no finite number of last terms of the error series tends to any finite or infinite values in this case.Keywords:
KW - asymptotical analysis
KW - linear signal
KW - separability
KW - signal processing
KW - singular spectral analysis
UR - http://www.scopus.com/inward/record.url?scp=85133681708&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/9ca73c56-d11c-3219-bc84-32914985895a/
U2 - 10.1134/S1063454122020157
DO - 10.1134/S1063454122020157
M3 - Article
VL - 55
SP - 166
EP - 173
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 2
ER -
ID: 96949284