On the Statistical Analysis of the Harmonic Signal Autocorrelation Function

International Journal of Applied Mathematics and Computer Science

Krajewski Mariusz¹  Sienkowski Sergiusz¹ 

[1] Institute of Metrology, Electronics and Computer Science, University of Zielona Góra, Szafrana 2, 65-516Zielona Góra, Poland;

关键词: harmonic signal;    autocorrelation function;    bias;    variance;    mean squared error;   

DOI  :  10.34768/amcs-2021-0050

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown