## 3 TF Transforms and Results
### Qualitative Data Analysis  
Due to the difficulty in the qualitative comparison of some transformations, a quantitative analysis was performed. For this purpose, the features extraction procedure was applied on the obtained TFRs. In Figure 5, the distribution of two selected parameters were shown as a function of angle \(\alpha\): the measure of the concentration of TFR--\(BN_{\text{TF,CM}}\) (on the left side) and the average value of TFR--\(BN_{\text{TF,MEAN}}\) (on the right side). The \(BN_{\text{TF,CM}}\) was chosen because it allows one to generalize the information contained in the TFR well. This parameter takes a higher value when the TFR is uniform. However, it is also insensible to low values of TFR. The second parameter, \(BN_{\text{TF,MEAN}}\), is a standard statistical parameter describing the average value of a distribution. The formulas of both parameters are presented in Table 4. The authors provided a wide description of possible methods of parametrization of TFR in their previous publication [19; 20]. Considering the angular \begin{table}
\begin{tabular}{c c} \hline \hline
**Transformation** & **Time (s)** \\ \hline STFT & 0.005556 \\ Wavelet & 0.073326 \\ FSST & 0.507287 \\ WSST & 0.634261 \\ SPWVDv1 & 0.175987 \\ SPWVDv2 & 0.219765 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Absolute computational times of each considered transformations for single MBN burst. \begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & **Model** \\ \hline CPU & AMD Ryzen 7 1800X Eight-Core 3.60 Hz \\ RAM & 32 GB 2900 MHz \\ GPU & GeForce GTX 1660 6 GB \\ HDD & ADATA XPG SX 8200 PNP M.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computer components configuration utilized in the computational process. distribution of the parameters obtained for the STFT spectrogram, the base approximation was determined. It was treated as a reference characteristic that allowed for a mutual comparison of the obtained TFRs by all considered transformations. To quantify the deviation between the characteristics of TF parameters and the reference approximation, the coefficient of determination \(r^{2}\) was calculated. The formula is given in Table 4, where \(y_{i}\) refers to the value of parameter for the \(i\)-th angle, \(\vec{y}_{i}\) is the value of approximation for \(i\)-th angle and \(\vec{y}\) is the average value of parameter. Data were normalized for each case to the [0, 1] range. As it can be seen in Figure 5, generally, both parameters'\(BN_{\text{TF\_CM}}\) and \(BN_{\text{TF\_Mean}}\)--values for all transformation increase while the angle is growing \(\alpha\) from \(0^{\circ}\) to \(90^{\circ}\). Then, both start to decrease. The characteristics of the TF parameters calculated from the STFT are highly correlated with the approximation (depicted with the blue continuous line on plot). In the case of other transformations, the significant local deviation from the approximation line can be clearly noticed, which may indicate a lower robustness of these transformations. In the case of SPWVDv2, a much more stable change in value relative to the angle was achieved than in case of SPWVDv1 as, along with increasing resolution both in frequency and time, the stability of the characteristics increases. The FSST-based characteristics have a similar trend as the ones for the STFT, although the values for the FSST-based TF parameters have a greater deviation from the approximation characteristic. In Figure 6, the bar plot showing the value of coefficient of determination \(r^{2}\) for both analyzed TF parameters is presented. For both parameters, the highest value of the \(r^{2}\) coefficient was achieved for the STFT. The lowest value was obtained for both versions of the SPWVD transformations. However, the coefficient \(r^{2}\) for the \(BN_{\text{TF\_MEAN}}\) parameter was higher by 28.32% for SPWVDv2 than for SPWVDv1. In the case of \(BN_{\text{TF\_CM}}\), this percentage difference was even greater and equal to 37.83%.