Asymptotical Separation of Polynomial Signals from Harmonics by Singular Spectrum Analysis

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Asymptotical Separation of Polynomial Signals from Harmonics by Singular Spectrum Analysis. / Nekrutkin, V. V.; Yakovlev, D. M.

In: Vestnik St. Petersburg University: Mathematics, Vol. 59, No. 2, 01.06.2026, p. 144-154.

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

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Nekrutkin, V. V. ; Yakovlev, D. M. / Asymptotical Separation of Polynomial Signals from Harmonics by Singular Spectrum Analysis. In: Vestnik St. Petersburg University: Mathematics. 2026 ; Vol. 59, No. 2. pp. 144-154.

BibTeX

@article{1c1493701a5e47b78fcde5b15bb6345e,

title = "Asymptotical Separation of Polynomial Signals from Harmonics by Singular Spectrum Analysis",

abstract = "Abstract: General approach to asymptotic signal extraction from an additively perturbed series with the help of Singular Spectrum Analysis (SSA) has already been described in [5]. This paper considers an example of this analysis applied to a polynomial signal and additive noise as linear combination of harmonics. In this case, the so-called reconstruction errors ri(N) of SSA have been found to uniformly tend to zero as the series length N tends to infinity. More precisely, we have proved that maxi |ri(N)| = O(N–1) as N → ∞ and for a “window length” L ~ αN, α ∈ (0, 1). This solves the problem of the accuracy of asymptotic separation of a polynomial signal from the seasonal component. The results on discrete Chebyshev polynomials in equally spaced points are essentially used to go to a polynomial of an arbitrary order from a linear signal, which was addressed for the case L = (N + 1)/2 in [7].",

keywords = "asymptotic analysis, discrete Chebyshev polynomials, polynomial signal, separability, signal processing, singular spectrum analysis",

author = "Nekrutkin, {V. V.} and Yakovlev, {D. M.}",

year = "2026",

month = jun,

day = "1",

doi = "10.1134/s1063454126700032",

language = "English",

volume = "59",

pages = "144--154",

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

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Asymptotical Separation of Polynomial Signals from Harmonics by Singular Spectrum Analysis

AU - Nekrutkin, V. V.

AU - Yakovlev, D. M.

PY - 2026/6/1

Y1 - 2026/6/1

N2 - Abstract: General approach to asymptotic signal extraction from an additively perturbed series with the help of Singular Spectrum Analysis (SSA) has already been described in [5]. This paper considers an example of this analysis applied to a polynomial signal and additive noise as linear combination of harmonics. In this case, the so-called reconstruction errors ri(N) of SSA have been found to uniformly tend to zero as the series length N tends to infinity. More precisely, we have proved that maxi |ri(N)| = O(N–1) as N → ∞ and for a “window length” L ~ αN, α ∈ (0, 1). This solves the problem of the accuracy of asymptotic separation of a polynomial signal from the seasonal component. The results on discrete Chebyshev polynomials in equally spaced points are essentially used to go to a polynomial of an arbitrary order from a linear signal, which was addressed for the case L = (N + 1)/2 in [7].

AB - Abstract: General approach to asymptotic signal extraction from an additively perturbed series with the help of Singular Spectrum Analysis (SSA) has already been described in [5]. This paper considers an example of this analysis applied to a polynomial signal and additive noise as linear combination of harmonics. In this case, the so-called reconstruction errors ri(N) of SSA have been found to uniformly tend to zero as the series length N tends to infinity. More precisely, we have proved that maxi |ri(N)| = O(N–1) as N → ∞ and for a “window length” L ~ αN, α ∈ (0, 1). This solves the problem of the accuracy of asymptotic separation of a polynomial signal from the seasonal component. The results on discrete Chebyshev polynomials in equally spaced points are essentially used to go to a polynomial of an arbitrary order from a linear signal, which was addressed for the case L = (N + 1)/2 in [7].

KW - asymptotic analysis, discrete Chebyshev polynomials

KW - polynomial signal

KW - separability

KW - signal processing

KW - singular spectrum analysis

UR - https://www.mendeley.com/catalogue/07176eda-4858-3794-b8f3-92ee1f501aa1/

U2 - 10.1134/s1063454126700032

DO - 10.1134/s1063454126700032

M3 - Article

VL - 59

SP - 144

EP - 154

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 153215681