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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 518, Pages 80–88
DOI: https://doi.org/10.31857/S2686954324040122 (Mi danma554) 		 
This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

A new spectral measure of complexity and its capabilities for detecting signals in noise

A. A. Galyaev, V. G. Babikov, P. V. Lysenko, L. M. Berlin

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russian Federation
Full-text PDF Citations (6)
DOI: https://doi.org/10.31857/S2686954324040122
Abstract: This article is devoted to the improvement of signal recognition methods based on information characteristics of the spectrum. A discrete function of the normalized ordered spectrum is established for a single window function included in the discrete Fourier transform. Lemmas on estimates of entropy, imbalance, and statistical complexity in processing a time series of independent Gaussian variables are proved. New concepts of one- and two-dimensional spectral complexities are proposed. The theoretical results were verified by numerical experiments, which confirmed the effectiveness of the new information characteristic for detecting a signal mixed with white noise at low signal-to-noise ratios.
Keywords: information entropy, spectral complexity, additive white Gaussian noise.
Funding agency Grant number
Russian Science Foundation 23-19-00134
This work was supported by the Russian Science Foundation (project no. 23-19-00134) and was performed at the Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences.
Received: 18.12.2023
Revised: 13.06.2024
Accepted: 05.07.2024
English version:
Doklady Mathematics, 2024, Volume 110, Issue 1, Pages 361–368
DOI: https://doi.org/10.1134/S1064562424702235
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: A. A. Galyaev, V. G. Babikov, P. V. Lysenko, L. M. Berlin, “A new spectral measure of complexity and its capabilities for detecting signals in noise”, Dokl. RAN. Math. Inf. Proc. Upr., 518 (2024), 80–88; Dokl. Math., 110:1 (2024), 361–368
Citation in format AMSBIB
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\by A.~A.~Galyaev, V.~G.~Babikov, P.~V.~Lysenko, L.~M.~Berlin
\paper A new spectral measure of complexity and its capabilities for detecting signals in noise
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 518
\pages 80--88
\mathnet{http://mi.mathnet.ru/danma554}
\crossref{https://doi.org/10.31857/S2686954324040122}
\elib{https://elibrary.ru/item.asp?id=74176083}
\transl
\jour Dokl. Math.
\yr 2024
\vol 110
\issue 1
\pages 361--368
\crossref{https://doi.org/10.1134/S1064562424702235}
Linking options:
  • https://www.mathnet.ru/eng/danma554
  • https://www.mathnet.ru/eng/danma/v518/p80
    Addendum
    This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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