On the statistical analysis of the harmonic signal autocorrelation function

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

International Journal of Applied Mathematics and Computer Science Pub Date : 2021-12-01 DOI:10.34768/amcs-2021-0050

S. Sienkowski, M. Krajewski

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引用次数: 1

Abstract

Abstract The article presents new tools for investigating the statistical properties of the harmonic signal autocorrelation function (ACF). These tools enable identification of the ACF estimator errors in measurements in which the triggering of the measurements is non-synchronized. This is important because in many measurement situations the initial phase of the measured signal is random. The developed tools enable testing the ACF estimator of a harmonic signal in the presence of Gaussian noise. These are the formulas on the basis of which the statistical properties of the estimator can be determined, including the bias, the variance and the mean squared error (MSE). For comparison, the article also presents the ACF statistical analysis tools used in the conditions of synchronized measurement triggering, known from the literature. Operation of the new tools is verified by simulation and experimental studies. The conducted research shows that differences between the MSE results obtained with the use of the developed formulas and those attained from simulations and experimental tests are not greater than 1 dB.

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谐波信号自相关函数的统计分析

摘要本文提出了研究谐波信号自相关函数(ACF)统计特性的新工具。这些工具能够在测量触发不同步的情况下识别测量中的ACF估计器错误。这一点很重要，因为在许多测量情况下，被测信号的初始相位是随机的。所开发的工具能够测试高斯噪声存在下谐波信号的ACF估计器。根据这些公式，可以确定估计器的统计特性，包括偏差、方差和均方误差(MSE)。为了比较，本文还介绍了文献中已知的同步测量触发条件下使用的ACF统计分析工具。通过仿真和实验验证了新工具的有效性。研究表明，利用所建立的公式得到的MSE结果与模拟和实验测试结果的差异不大于1 dB。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Applied Mathematics and Computer Science 工程技术-计算机：人工智能

CiteScore

4.10

自引率

21.10%

发文量

审稿时长

4.2 months

期刊介绍： The International Journal of Applied Mathematics and Computer Science is a quarterly published in Poland since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland (Sciendo) and Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences. The journal strives to meet the demand for the presentation of interdisciplinary research in various fields related to control theory, applied mathematics, scientific computing and computer science. In particular, it publishes high quality original research results in the following areas: -modern control theory and practice- artificial intelligence methods and their applications- applied mathematics and mathematical optimisation techniques- mathematical methods in engineering, computer science, and biology.