On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis

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On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis. / Зенкова, Наталья Валентиновна; Некруткин, Владимир Викторович.

In: Vestnik St. Petersburg University: Mathematics, Vol. 55, No. 2, 01.06.2022, p. 166-173.

Research output: Contribution to journal › Article › peer-review

Author

Зенкова, Наталья Валентиновна ; Некруткин, Владимир Викторович. / On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis. In: Vestnik St. Petersburg University: Mathematics. 2022 ; Vol. 55, No. 2. pp. 166-173.

BibTeX

@article{87b983965bdf4181a30bb966c304ca81,

title = "On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis",

abstract = "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:",

keywords = "asymptotical analysis, linear signal, separability, signal processing, singular spectral analysis",

author = "Зенкова, {Наталья Валентиновна} and Некруткин, {Владимир Викторович}",

note = "Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = jun,

day = "1",

doi = "10.1134/S1063454122020157",

language = "English",

volume = "55",

pages = "166--173",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - On the Asymptotical Separation of Linear Signals from Harmonics by Singular Spectrum Analysis

AU - Зенкова, Наталья Валентиновна

AU - Некруткин, Владимир Викторович

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