## 5 Measurement Verification of the Effectiveness of the Proposed Method  
The measurement verification of the effectiveness of the discussed method was performed on the measurement chain, the error model and metrological properties of which were described in [16]. A schematic diagram is shown in Figure 7. This measurement chain processes the time-varying voltage \(s(t)\in[0;1]\) V, which is first conditioned by the A/A processing system into the signal \(y(t)\) and then converted into the form \(x(i)\) by the A/D converter. The analyzed quantity \(x(i)\) is defined as follows:  
\[\dot{x}(i)=s_{x,x}\dot{s}(iT_{s})=\dot{s}(iT_{s}), \tag{47}\] \[\ddot{x}(i)=\dot{s}\Big{(}iT_{p}\Big{)}+e_{x,\Sigma}(i), \tag{48}\]  
where \(T_{s}\) is the sampling period corresponding to the sampling frequency \(f_{s}=48\) kHz, and \(e_{x,\Sigma}(i)\) is the resultant error signal of magnitude \(x(i)\), which consists of the following:  
* \(e_{x,r}(i)\)--resultant random error signal with constant power spectral density, zero expected value, normally distributed realization values, and variance of 0.13 \(\mu\)V\({}^{2}\),
* \(e_{x,d}(i)\)--resultant dynamic error signal, whose variance values \(\sigma_{x,d,k}^{2}\) for subsequent harmonics is estimated using the proposed method.  
According to the considerations in [16], the origin of the dynamic error signal \(e_{x,d}(i)\) for the discussed measurement chain is the imperfect dynamics of the operational amplifier operating in a non-inverting configuration, whose cutoff frequency is about 165 kHz. This component introduces a significant phase shift:  
\[\ddot{\phi}_{y}(\omega)\approx-6.26\cdot 10^{-13}\omega^{2}-5.73\cdot 10^{-7}\omega, \tag{49}\]  
for a harmonic with angular frequency \(\omega\), where for the ideal measurement task, \(\phi_{y}(\omega)=0\) rad. Regarding gain values, it can be assumed that for frequencies in the range \([0;\frac{1}{2}f_{s}]\), \(\ddot{R}_{y}(\omega)\cong\ddot{K}_{y}(\omega)=3.29\) V/V holds.  
Therefore, the information presented in [16] concerning the metrological properties of the analyzed measurement chain allows direct application of the proposed method to estimate the variance of the dynamic error signal. In this section of the paper, the proposed  
Figure 7: Schematic diagram of the analyzed measurement chain (source: [16] under the CC BY 4.0 license).  
algorithm is applied to the quantity \(x(i)\), which in this case is the input to the Discrete Wavelet Transform (DWT) algorithm.  
For the given parameters of the signal \(s(t)\), 30,000 sets of \(N=128\) subsequent values of the realization of the quantity \(x(i)\) were collected, with the initial phase of the signal \(s(t)\) randomized. The proposed method for estimating the variance \(\sigma_{e}^{2}\) of the dynamic error signal was applied to the obtained samples. Then, the trajectory/realization/behavior of the error signal \(e_{x,\Sigma}(i)\) and its variance \(\sigma_{x,\Sigma}^{2}\) were estimated according to Equation (48), based on which the actual value \(\sigma_{s}^{2}\) of the variance of the dynamic error signal was estimated:  
\[\sigma_{s}^{2}=\sigma_{x,\Sigma}^{2}-\sigma_{x,r}^{2}. \tag{50}\]  
It should be noted that the variance estimated according to Equation (50) may be higher in practice than the actual variance of the dynamic error signal \(e_{x,d}(i)\). This equation assumes that, apart from the errors mentioned in the Introduction, there are no other significant sources of error. This assumption may not be entirely accurate, but without knowledge of the exact error model of the entire measurement chain, determining the exact value of this parameter is not possible.