## 4 Simulation Verification of the Method
### The Case of Spectrum Leakage
This phenomenon is discussed in more detail later in the paper. As mentioned in the Introduction, the phenomenon of spectral leakage can be mitigated by using an appropriate measurement window. The experiment discussed so far was repeated using the following measurement windows: \"Blackman\", \"Hamming\", \"Bartlett\", \"Hann\", and \"Flat Top\" [42], in accordance with Equation (33). The experiment was conducted under conditions identical to those in the previous case, with the only difference being the use of a constant input quantity vector length of \(N=64\). Selected experimental results are presented in Table 2 and Figure 4. The experiment can be reproduced by running the script in the file case_2_window.m, located in the repository [47]. Based on the presented results, it can be concluded that when the conditions of coherent sampling are met, the inaccuracy in estimating the variance of the dynamic error signal is greater than in the case without a measurement window. The measurement window used under coherent sampling causes the phenomenon of spectrum blurring. In the case of non-coherent sampling, the value of the discussed parameter is significantly smaller. It should be noted that, in practical measurements, achieving full sampling coherence is not possible. The use of a measurement window is therefore justified, despite the mentioned negative effects. The introduced error is small, while the inaccuracy in non-coherent sampling is significantly reduced. Of all the measurement windows used, the \"Flat Top\" window showed the lowest effectiveness. The \"Bartlett\", \"Hann\", \"Blackman\", and \"Hamming\" windows showed similar effectiveness. It can therefore be concluded that, for the analyzed case, dynamics are more important than window resolution. By analyzing the statistical parameters of the obtained results, it can also be observed that the \"Blackman\" and \"Flat Top\" windows show almost zero dispersion in the relative error of estimating the variance. Because the \"Hamming\" measurement window showed the greatest effectiveness for the analyzed case, it is used throughout the remainder of this paper. Given the results of the previous experiment, where 95% of the relative error values in estimating the variance for \(N=64\) were within the range \([0;39]\%\), while in the experiment using a measurement window this range narrowed to \([-0.7;2.8]\%\) for the \"Hamming\" window, it is clear that the use of a measurement window significantly improves the accuracy of the obtained results. It should be emphasized, however, that in the first experiment, the overestimated variance values concerned cases where the variance was  
Figure 4: The values of the quantity \(\delta\) (34) for the input signal described by Equation (37) (selected cases using a window function, with expanded uncertainty at a 95% confidence level). very small compared to other more accurately estimated cases, which may be insignificant in the background of other error signals. Therefore, the advantages and disadvantages of using a measurement window should be considered in terms of computational complexity and potential impact on the accuracy of the obtained results. This topic is further discussed later in the paper.