## 2 Experimental Setup
From each measurement, 10 MBN bursts were extracted. A schematic of the measurement system is shown in Figure 4.  
Figure 4: Schematic of the measurement system. Figure 3: View of the transducer and schematics illustration of the measuring procedure; RD—rolling direction of steel; TD—transverse direction of the steel. In the next step, the acquired MBN signals were transformed to the time-frequency space using STFT. A window with the Kaiser function of different sizes was used for the calculations:  
\[w(n)=\frac{I_{0}\left(\beta\sqrt{\left(\frac{n-\frac{N}{2}}{\beta}\right)} \right)}{I_{0}} \tag{1}\]  
where \(I_{0}\) is the Bessel function of zero order and \(\beta\) is its parameter, \(n\) is a given sample and \(N\) is the size of the window \(w\). The Kaiser function is characterized by the ability to adjust the width of the main lobe and the attenuation of the side lobes (parameter \(\beta\) equal 0.5 in this case), which enables it to be adapted to the specific requirements of the analysis. The window is close to the spheroidal window, which maximizes the ratio of the energy of the main lobe to the energy of the side lobes, resulting in reduced spectral leakage and improved spectral resolution [42]. A discussion on the choice of window function was given in previous article [38]. The Preparation of MBN Databases Used to Perform the Analysis of Time-Frequency Window Size on CNN Accuracy  
Two major sets of data consisting of appropriately computed spectrograms were prepared for the experiment. Each database was developed with the same proportions: 80% training set, 10% validation set, and 10% testing set. Each of the databases contained 260 classes, which refers to 26 classes (26 transducer angular positions over the sample surface) for each out of the 10 samples tested. The first type of database consisted of four individual sub-databases, each obtained from processing the MBN signal with STFT using a different window size (128, 256, 512, 1024). In addition, windowing overlap options of 75% were used and enabled increasing resolution in time [38]. The effective resolution values of the spectrograms obtained using STFT over time and frequency are shown in Table 2. Considering the magnetizing field frequency of 10 Hz, a single MBN burst covers a period corresponding to 50 ms. On this basis, it can be seen that the greatest generalization of the characteristic in time can be obtained for a window of 1024 and in the frequency for a window of 128. The essence of the experiments is therefore to compare whether the generalization process taking place for different window sizes during the calculation of spectrograms leads to significant distortions of the key information on the state of the material contained in the spectrograms. Example spectrogram results obtained using different window sizes for a selected sample and different transducer angular alignments in relation to the rolling direction are shown in Figures 5 and 6. In Figure 5, the influence of the change in the magnetization angle and the observation of the Barkhausen effect in relation to the steel rolling direction can be seen. It can be seen that the smallest activity is visible when the transducer is oriented in the TD direction (0\({}^{\circ}\)) and with the rotation to the RD direction, the MBN energy clearly increases (as a result of a larger number of 180 domains in the RD direction). However, already for directions convergent with the TD angle, one can notice visible spatialization of MBN activity in time and frequency. The first region is visible for approximately 15 ms, and the second between 30 and 40 ms. With the increase in the measuring angle, another region becomes visible between the two mentioned above. Shifts in time and increases in energy of the mentioned regions are clearly visible, depending on the measurement angle.