1. bookVolume 31 (2021): Issue 4 (December 2021)
    Advanced Machine Learning Techniques in Data Analysis (special section, pp. 549-611), Maciej Kusy, Rafał Scherer, and Adam Krzyżak (Eds.)
Journal Details
License
Format
Journal
eISSN
2083-8492
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
access type Open Access

On the statistical analysis of the harmonic signal autocorrelation function

Published Online: 30 Dec 2021
Page range: 729 - 744
Received: 31 May 2021
Accepted: 04 Oct 2021
Journal Details
License
Format
Journal
eISSN
2083-8492
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
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.

Keywords

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