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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2024 Volume 518, Pages 80–88 (Mi danma554)

This article is cited in 4 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

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.

UDC: 517.54

Received: 18.12.2023
Revised: 13.06.2024
Accepted: 05.07.2024

DOI: 10.31857/S2686954324040122


 English version:
Doklady Mathematics, 2024, 110:1, 361–368

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© Steklov Math. Inst. of RAS, 2025