## 5 Application of the Proposed Analysis Method
In considering the aforementioned relationships, in the scenario of a sinusoidally varying signal \(s(t)\), the resulting error signal \(e_{x,\Sigma,sin}(i)\) will comprise the signal \(e_{x,r}(i)\) and the signal \(e_{x,d,sin}(i)\) consisting of a single harmonic with pulsation \(\omega_{s,\rho}\). In the instance of a triangular signal, the error signal \(e_{x,\Sigma,tri}(i)\) will also encompass a random error component \(e_{x,r}(i)\), and depending on the signal's pulsation \(s(t)\), it will include a specific number of harmonics of the random error signal \(e_{x,d,tri}(i)\), where the \(i\)-th harmonic is characterized by a pulsation of \(\omega_{x,\varepsilon,i}=(2i-1)\omega_{s,\rho}\). These error signals discussed will be propagated to the algorithm output as per Equation (1). The parameters at the algorithm output can be determined for subsequent output quantities following Equation (6) for the random error signals and Equation (5) for the successive harmonics of the resultant dynamic error signal. Moreover, in the scenarios discussed, the WT algorithm will introduce its own error signals \(e_{X,z,i}(j)\) to the output values, linked to the previously mentioned roundings. The vector of expanded uncertainties related to the resultant error signal for subsequent output quantities of the algorithm, as required in Equation (39), can thus be delineated as  
\[\mathbf{U}_{s,sin}=\Big{[}U_{s,z}\quad U_{s,r}\quad U_{s,d,sin}\Big{]},\]in the case of a sinusoidal signal, and in the case of a triangular signal, in the following form:  
\[\mathbf{U}_{s,tri}=\Big{[}U_{s,\boldsymbol{\tau}}\quad U_{s,\boldsymbol{\tau}} \quad U_{s,d,tri,1}\quad U_{s,d,tri,2}\quad\ldots\quad U_{s,d,tri,N}\Big{]}.\]  
The symbol \"\(*\)\" represents the output quantity number, assigned following the symbols introduced earlier in Equation (8). Based on the previously addressed characteristics of the WT algorithm, for random error signals, the uncertainty linked to the propagation of these signals to the WT algorithm's output can be calculated using the following relationship:  
\[U_{s,\boldsymbol{\tau}}=c_{n}\sigma_{x,\boldsymbol{\tau}}\sqrt{\sum_{j=0}^{N-1 }a_{s,j}^{2}},\]  
resulting from Equation (6), while in the case of the subsequent harmonics of the resultant dynamic error signal,  
\[U_{s,\boldsymbol{\mu}}(\omega)=c_{d}\sigma_{x,\boldsymbol{\mu}}(\omega) \bigg{|}H_{*}\Big{(}\mathrm{e}^{\mathrm{i}\omega T_{s}}\Big{)}\bigg{|}=c_{d} \frac{1}{\sqrt{2}}E_{x,\boldsymbol{\tau}}(\omega)\bigg{|}H_{*}\Big{(}\mathrm{e }^{\mathrm{i}\omega T_{s}}\Big{)}\bigg{|},\]  
which results from Equation (5). The resulting expanded uncertainty \(U_{s,\Sigma}\) related to the subsequent output quantities can be determined according to Equation (39), with the values of the coherence coefficients estimated based on relationship (40). For the confidence level \(1-\alpha=95\%\,c_{n}=1.96\) and \(c_{d}=1.41\)[40], \(c_{z}=2.15\). To validate the indicated relationships, a Monte-Carlo measurement experiment was conducted, gathering 30,000 values of the \(X_{*}(j)\) signal realization each time. Throughout the experiment, the signal source \(s(t)\) originated from the RIGOL DG1011 arbitrary waveform generator [47]. The initial phase of this signal was randomized within the interval \([-\pi;\pi]\), which was determined using the generator's synchronizing output. The signal's frequency \(s(t)\) ranged from \(\hat{f}_{s,\rho}\in[1;20]\) kHz for a monoharmonic signal and from \(\hat{f}_{s,\rho}\in[1;5]\) kHz for a polyharmonic signal.