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A new spectral measure of complexity and its capabilities for detecting signals in noise
- Authors: Galyaev A.A.1, Babikov V.G.1, Lysenko P.V.1, Berlin L.M.1
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Affiliations:
- Institute of Control Sciences of RAS
- Issue: Vol 518, No 1 (2024)
- Pages: 80-88
- Section: MATHEMATICS
- URL: https://kazanmedjournal.ru/2686-9543/article/view/648005
- DOI: https://doi.org/10.31857/S2686954324040122
- EDN: https://elibrary.ru/YYEJZI
- ID: 648005
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Abstract
This article is devoted to the improvement of signal recognition methods based on the information characteristics of the spectrum. A discrete function of the normalized ordered spectrum is established for a single window function included in the DFT. Lemmas on estimates of entropy, imbalance and statistical complexity in processing a time series of independent Gaussian quantities are proved. New concepts of one-dimensional and two-dimensional spectral complexities are proposed. The theoretical results obtained were verified by numerical experiments, which confirmed the effectiveness of the new information characteristic when detecting a signal mixed with white noise at low signal-to-noise ratios.
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About the authors
A. A. Galyaev
Institute of Control Sciences of RAS
Author for correspondence.
Email: galaev@ipu.ru
Corresponding Member of the RAS
Russian Federation, MoscowV. G. Babikov
Institute of Control Sciences of RAS
Email: babikov@ipu.ru
Russian Federation, Moscow
P. V. Lysenko
Institute of Control Sciences of RAS
Email: pavellysen@ipu.ru
Russian Federation, Moscow
L. M. Berlin
Institute of Control Sciences of RAS
Email: berlin.lm@phystech.edu
Russian Federation, Moscow
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