Asymptotical Separation of Harmonics by Singular Spectrum Analysis

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Asymptotical Separation of Harmonics by Singular Spectrum Analysis. / Некруткин, Владимир Викторович.

In: Vestnik of the St. Petersburg University: Mathematics, Vol. Vol. 56, No. 4, 12.2023, p. 720–735.

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

BibTeX

@article{55daeee1b47c414db3afe8522abba3ad,

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

abstract = "The paper is devoted to studying the sufficient conditions for the asymptotical separability of distinct terms in the linear combination of harmonics by singular spectrum analysis (SSA). Namely, the series x_0, …, with x_n =\sum_{i=1}^r b_i cos(\omega_i n + \gamma_i) where both amplitudes |b_i| and frequenciesω_i ∈ (0, 1/2) are pairwise different, are considered. Then, as is proved in this study, under some relationship between amplitudes |b_i| and the choice of standard SSA parameters, the so-called reconstructed values prove to be very close to for large N. ",

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

author = "Некруткин, {Владимир Викторович}",

year = "2023",

month = dec,

doi = "10.1134/S1063454123040118",

language = "English",

volume = "Vol. 56",

pages = "720–735",

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

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - Asymptotical Separation of Harmonics by Singular Spectrum Analysis

AU - Некруткин, Владимир Викторович

PY - 2023/12

Y1 - 2023/12

N2 - The paper is devoted to studying the sufficient conditions for the asymptotical separability of distinct terms in the linear combination of harmonics by singular spectrum analysis (SSA). Namely, the series x_0, …, with x_n =\sum_{i=1}^r b_i cos(\omega_i n + \gamma_i) where both amplitudes |b_i| and frequenciesω_i ∈ (0, 1/2) are pairwise different, are considered. Then, as is proved in this study, under some relationship between amplitudes |b_i| and the choice of standard SSA parameters, the so-called reconstructed values prove to be very close to for large N.

AB - The paper is devoted to studying the sufficient conditions for the asymptotical separability of distinct terms in the linear combination of harmonics by singular spectrum analysis (SSA). Namely, the series x_0, …, with x_n =\sum_{i=1}^r b_i cos(\omega_i n + \gamma_i) where both amplitudes |b_i| and frequenciesω_i ∈ (0, 1/2) are pairwise different, are considered. Then, as is proved in this study, under some relationship between amplitudes |b_i| and the choice of standard SSA parameters, the so-called reconstructed values prove to be very close to for large N.

KW - signal processing, singular spectral analysis, linear combination of harmonics, separability of harmonics, asymptotical analysis

U2 - 10.1134/S1063454123040118

DO - 10.1134/S1063454123040118

M3 - Article

VL - Vol. 56

SP - 720

EP - 735

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 115398106