title: On the asymptotical separation of linear signals from harmonics by singular spectrum analysis
metadata.name: dc.contributor.author
metadata.value: Zenkova, Natalia V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Nekrutkin, Vladimir V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-07T21:26:33Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-07T21:26:33Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zenkova N.V., Nekrutkin V.V. On the asymptotical separation of linear signals from harmonics by singular spectrum analysis. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 245–254.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.206
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37104
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The general theoretical approach to the asymptotic extraction of the signal series from the
  additively perturbed signal with the help of singular spectrum analysis (briefly, SSA) was
  already outlined in Nekrutkin (2010), SII, vol. 3, 297–319. In this paper we consider the
  example of such an analysis applied to the linear signal and the additive sinusoidal noise.
  It is proved 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) if N → ∞ and the “window length” L equals (N + 1)/2. It is
  important to mention, that the completely different result is valid for the increasing exponential
  signal and the same noise. As it is proved in Ivanova, Nekrutkin (2019), SII, vol. 12,
  1, 49–59, in this case any finite number of last terms of the error series does not tend to
  any finite or infinite values.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The study was supported by the Russian Foundation for Basic Research (project no. 20-01-00067).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9 (67); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: signal processing
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: singular spectral analysis
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: separability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linear signal
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotical analysis
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the asymptotical separation of linear signals from harmonics by singular spectrum analysis
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 245-254.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37104/1/245-254.pdf
resources.format: Adobe PDF
resources.size: 542,65 kB