<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

On the statistical analysis of the harmonic signal autocorrelation function

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the statistical analysis of the harmonic signal autocorrelation function"}

The article presents new tools for investigating the statistical properties of the harmonic signal autocorrelation function (ACF). These tools enable...

On the statistical analysis of the harmonic signal autocorrelation function

Published Online: Dec 30, 2021

Page range: 729 - 744

Received: May 31, 2021

Accepted: Oct 04, 2021

DOI: https://doi.org/10.34768/amcs-2021-0050

Keywords
harmonic signal, autocorrelation function, bias, variance, mean squared error

© 2021 Sergiusz Sienkowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the statistical analysis of the harmonic signal autocorrelation function

Published Online: Dec 30, 2021

Page range: 729 - 744

Received: May 31, 2021

Accepted: Oct 04, 2021

DOI: https://doi.org/10.34768/amcs-2021-0050

Keywordsharmonic signal, autocorrelation function, bias, variance, mean squared error

© 2021 Sergiusz Sienkowski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
harmonic signal, autocorrelation function, bias, variance, mean squared error