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

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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.

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, Moscow

V. 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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