## 4 Method for Determining the Resultant Expanded Uncertainty  
In many cases, merely knowing the value of the standard uncertainty parameter or the error signal variance may not suffice [40]. The most universal method used to determine the resulting expanded uncertainty value in a general situation is the Monte-Carlo method. However, this approach necessitates numerous iterations to obtain the final value of the analyzed error signal and may not be suitable for the real-time evaluation of the metrological properties of the measurement chain due to the time required to repeat the experiment. An alternative to the Monte-Carlo method could be an analytical method, such as the propagation of distribution functions method described in sources like [41] or the extended rule of the combination of uncertainties method outlined in [42]. However, these methods are intricate, and their application to the error model proposed in this study might be less effective compared to the reduction interval arithmetic method, as discussed in works like [43; 44; 45]. Another alternative could be a method based on fuzzy logic, as detailed in [46]. Due to the advantages of the interval arithmetic reduction method, such as its simplicity of application, its ability to determine new values of the resulting expanded uncertainty when the error model parameters change without the need for a Monte-Carlo experiment, and its low computational complexity, the reduction interval arithmetic method was employed to ascertain the resulting value of the expanded uncertainty in this study. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Quantity**} & \multicolumn{6}{c}{**WT Algorithm Input Values Range**} \\  & \([-1;1]\) & \([-2;2]\) & \([-3;3]\) & \([0;2]\) & \([0;4]\) & \([3;9]\) \\ \hline \(S_{2,0}\) & \(1.40\times 10^{-15}\) & \(5.57\times 10^{-15}\) & \(1.30\times 10^{-14}\) & \(9.29\times 10^{-15}\) & \(3.71\times 10^{-14}\) & \(2.78\times 10^{-13}\) \\ \(S_{2,1}\) & \(1.40\times 10^{-15}\) & \(5.61\times 10^{-15}\) & \(1.29\times 10^{-14}\) & \(1.25\times 10^{-14}\) & \(5.00\times 10^{-14}\) & \(3.54\times 10^{-13}\) \\ \(T_{2,0}\) & \(1.71\times 10^{-15}\) & \(6.83\times 10^{-15}\) & \(1.58\times 10^{-14}\) & \(3.33\times 10^{-15}\) & \(1.33\times 10^{-14}\) & \(7.78\times 10^{-14}\) \\ \(T_{2,1}\) & \(1.39\times 10^{-15}\) & \(5.56\times 10^{-15}\) & \(1.29\times 10^{-14}\) & \(4.27\times 10^{-15}\) & \(1.71\times 10^{-14}\) & \(1.16\times 10^{-13}\) \\ \(T_{1,0}\) & \(8.28\times 10^{-16}\) & \(3.54\times 10^{-15}\) & \(8.38\times 10^{-15}\) & \(1.70\times 10^{-15}\) & \(6.84\times 10^{-15}\) & \(4.25\times 10^{-14}\) \\ \(T_{1,1}\) & \(6.82\times 10^{-16}\) & \(2.72\times 10^{-15}\) & \(6.67\times 10^{-15}\) & \(1.46\times 10^{-15}\) & \(5.84\times 10^{-15}\) & \(4.02\times 10^{-14}\) \\ \(T_{1,2}\) & \(6.82\times 10^{-16}\) & \(2.72\times 10^{-15}\) & \(6.66\times 10^{-15}\) & \(1.47\times 10^{-15}\) & \(5.86\times 10^{-15}\) & \(4.02\times 10^{-14}\) \\ \(T_{1,3}\) & \(6.68\times 10^{-16}\) & \(2.67\times 10^{-15}\) & \(6.48\times 10^{-15}\) & \(2.02\times 10^{-15}\) & \(8.10\times 10^{-15}\) & \(6.15\times 10^{-14}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of the simulation-obtained values of the rounding error signal variance of subsequent output quantities of the discrete wavelet transform algorithm for the wavelet “db2” with two iterations of the decomposition process, for numbers with a length of 32 bits, depending on the range of possible values of the implementation of the input quantitiesAccording to the method of reduction interval arithmetic, the expanded uncertainty in case of an error signal \(e_{\Sigma}(t)=e_{0}+\ldots+e_{N-1}\) can be determined according to the following relation [43; 44]:  
\[U_{\Sigma}=\sqrt{\left[ \begin{array}{c}U_{0}\\ U_{1}\\ \vdots\\ U_{N-1}\end{array} \right]^{T}\left[ \begin{array}{ccccc}1&h_{0,1}&\cdots&h_{0,N-1}\\ h_{1,0}&1&&h_{1,N-1}\\ \vdots&&\ddots&\vdots\\ h_{N-1,0}&\cdots&\cdots&1\end{array} \right]\left[ \begin{array}{c}U_{0}\\ U_{1}\\ \vdots\\ U_{N-1}\end{array}