## 5 Application of the Proposed Analysis Method  
The effectiveness of the proposed analysis method was verified using the measurement chain detailed in a previous study [19]. This measurement chain processes a time-varying voltage signal \(s(t)\), with realization values falling within the range \(\hat{s}(t)\in[0;1]\) V on discrete representations of \(x(i)\) of this magnitude, where \(x(i)=s(iT_{s})\), and \(f_{s}=\frac{1}{T_{s}}=48\) kHz denotes the sampling period. In a single measurement series, with \(N=8\), consecutive samples of quantities \(x(i)\) are inputted into the WT algorithm described in the previous \begin{table}
\begin{tabular}{c c c c c c} \hline \(s_{a,b}\) & \(\mathbf{n}\) & \(\mathbf{u}\) & \(\mathbf{t}\) & \(\mathbf{d}\) & \(\mathbf{z}\) \\ \hline \(n\) & 0.0000 & 0.1561 & 0.0250 & 0.2988 & \(-\)0.0091 \\ \(\mathbf{u}\) & 0.1561 & 0.3356 & 0.1773 & 0.5337 & 0.0662 \\ \(\mathbf{t}\) & 0.0250 & 0.1773 & 0.0419 & 0.3504 & \(-\)0.0104 \\ \(\mathbf{d}\) & 0.2988 & 0.5337 & 0.3504 & 0.7136 & 0.1971 \\ \(\mathbf{z}\) & \(-\)0.0091 & 0.0662 & \(-\)0.0104 & 0.1971 & 0.0273 \\ \hline \end{tabular}
\end{table} 
Table 3: Summary of shape factor values for pairs of signals with typical probability density functions for the confidence level 95%, where the following symbols denote a distribution: \((n)\) normal, \((u)\) uniform, \((t)\) triangular, \((d)\) u-shape (sine function distribution), \((z)\) WT self-error signal distribution. section, leading to the determination of a vector \(M=8\) of output quantities \(X(j)\). The algorithm's implementation utilizes floating-point numbers with a word length of 32 bits. The metrological properties of the section of the measurement chain responsible for converting the quantity \(s(t)\) into \(x(i)\) were previously discussed in [19]. The uncertainty budget related to \(x(i)\) encompasses the random error signal \(e_{x,r}(i)\) and the dynamic error signal \(e_{x,d}(i)\). For the random error signal \(e_{x,r}(i)\), the variance is \(\sigma^{2}_{x,r}=0.13\,\upmu\)V, and the realization values of this signal are distributed close to normal. Hence, for a confidence level of \(1-\alpha=95\%\), the coverage factor \(c_{x,r}=c_{n}=1.96\), and the expanded uncertainty is \(U_{x,r}=0.71\) mV. Regarding the dynamic error signal \(e_{x,d}(i)\), its characteristics are influenced by the spectrum of the processed signal \(s(t)\). If this signal is a sinusoidally varying signal with pulsation \(\omega_{s,\rho}\) and amplitude \(E_{s,\rho}\), the following conditions apply [19]:  
\[\sigma^{2}_{x,d,sin}=\frac{\left(E_{s,\rho}\cos\left(\widehat{\varphi}_{y} \big{(}\omega_{s,\rho}\big{)}\right)-E_{s,\rho}\right)^{2}+\left(E_{s,\rho} \sin\left(\widehat{\varphi}_{y}\big{(}\omega_{s,\rho}\big{)}\right)\right)^{ 2}}{2},\]  
however, if the signal is a triangular signal with the given parameters, then [19]:  
\[\sigma^{2}_{x,d,tri}=\sum_{i=1}^{\infty}\sigma^{2}_{x,d,tri,i},\]  
\[\sigma^{2}_{x,d,tri,i}=\frac{\left(E_{s,\rho,i}\cos\left(\widehat{\varphi}_{y }\big{(}\omega_{s,\rho,i}\big{)}\right)-E_{s,\rho,i}\right)^{2}+\left(E_{s, \rho,i}\sin\left(\widehat{\varphi}_{y}\big{(}\omega_{s,\rho,i}\big{)}\right) \right)^{2}}{2}, \tag{41}\]  
\[E_{s,\rho,i}=\frac{\pi}{8}(2i-1)^{-2}E_{s,\rho},\]  
where in Equation (41), only those harmonics of the signal \(s(t)\) for which \(kf_{s,\rho}\leq\frac{1}{2}f_{s}\) holds are taken into account, where \(k=(2i-1)\). The introduced phase shift \(\widehat{\varphi}_{y}\), which is the origin of the dynamic error signal, is estimated according to the relationship [19]  
\[\widehat{\varphi}_{y}(\omega)\approx-6.26\times 10^{-13}\omega^{2}-5.73\times 1 0^{-7}\omega.\]  
As the ambient conditions did not change during the experiments, it is assumed that the static error signal \(e_{x,s}(i)\) does not occur.