## 5 Measurement Verification of the Effectiveness of the Proposed Method
### Analysis of the Obtained Measurement Results  
In analyzing the results of the conducted experiments, it can be seen that the proposed method is suitable for use with a typical measurement chain built using a \"system-on-chip\" solution. For selected experimental conditions, the relative error in estimating the variance value exceeds \(\pm 10\%\), but it should be emphasized that a similar magnitude of discrepancies was observed using the analytical method in [16]. As in the cited work, the cause of the discrepancy between the obtained results is the inaccuracy in determining the parameters of the error model of the analyzed measurement chain and the presence of additional error signals, the parameters of which were not estimated accurately enough or were completely omitted, being considered insignificant. By comparing the results of the measurement and simulation experiments, it can be seen that in the simulation case, the expected value of the estimated parameter was \begin{table}
\begin{tabular}{c c c c} \hline \(f_{s,o},\mathrm{kHz}\) & \(\sigma_{s}^{2},\mathrm{\mu V}^{2}\) & \(\sigma_{e}^{2},\mathrm{\mu V}^{2}\) & \(\overline{\delta},\%\) \\ \hline
1 & 1.07 & 1.35 & \(26.0\pm 2.0\) \\
2 & 5.18 & 5.02 & \(-3.2\pm 6.0\) \\
3 & 9.93 & 11.3 & \(14\pm 10\) \\
4 & 21.1 & 20.1 & \(-5\pm 12\) \\
5 & 34.2 & 30.9 & \(-9.70\pm 0.53\) \\ \hline \end{tabular}
\end{table} 
Table 5: Results \({}^{\star}\) of the measurement experiment for the case of the polyharmonic signal \(s(t)\) described in Equation (51) (with expanded uncertainty at a 95% confidence level). Figure 9: Histograms of the realization values of the relative error in estimating the variance of the dynamic error signal (selected cases of polyharmonic signal, with expanded uncertainty at a 95% confidence level). consistently very close to the true value. The variability of this value, and consequently the relative error dispersion, resulted from confounding factors discussed in the description of the experiments. Therefore, it can be concluded that in the measurement experiment, the non-zero expected value of the relative estimation error does not arise from the properties or specificity of the proposed method. In the case of the applied measurement chain, the DWT algorithm was used, the implementation of which was made in the matrix form as show in [51]. The output quantities of the algorithm were determined according to the method described in the work [18], using for this purpose the function arm_mat_mult_f32 contained in the CMSIS-DSP [4] library. At a sampling frequency of 48 kHz, collecting the vector \(N=128\) of input quantities \(x(i)\) needed to perform a single iteration of the measurement of the used algorithm took 2.67 ms, while the time needed to determine the vector of output quantities of this algorithm was 1.85 ms. The realization of Equation (20) was implemented using the arm_rfft_fast_f32 function of the CMSIS-DSP [4] library, where the time required to perform the calculations was 0.069 ms. The time required to estimate the variance value according to Equation (28) was 0.086 ms, where Equation (21) was implemented using the arm_cmplx_mag_f32 function of the CMSIS-DSP [4] library. It can therefore be seen that in the presented measurement system, the proposed method can be used in real time. The source code of the program used in the discussed measurement system can be found in [52] repository. An alternative to using the matrix form of the algorithm can be a recursive implementation, in which the wavelet transform algorithm is treated as a pair of filters [7]. This approach was used in the [53] library, where for the case of the analyzed measurement chain, the time needed to implement the wavelet transform algorithm using the discussed method is 0.981 ms. It should be noted here that the originally proposed method presenting the wavelet transform algorithm in the matrix form is much more universal and simpler to implement, which is why it is more user-friendly for the measurement chain designer than the solution proposed in [53].