复杂性的新频谱测量方法及其在噪声中检测信号的能力

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-10-20 DOI:10.1134/S1064562424702235

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

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引用次数: 0

摘要

本文致力于改进基于频谱信息特征的信号识别方法。针对离散傅里叶变换中包含的单窗函数，建立了归一化有序频谱的离散函数。证明了处理独立高斯变量时间序列时的熵估计、不平衡和统计复杂性的定理。提出了一维和二维频谱复杂性的新概念。数值实验验证了理论结果，证实了新的信息特征在低信噪比条件下检测混有白噪声的信号的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise

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A New Spectral Measure of Complexity and Its Capabilities for Detecting Signals in Noise

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.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.