## 2 Experimental Setup  
The experiment was carried out for GO electrical steel sheets. The parameters of the utilized steels are shown in Table 1.  
As can be seen (Table 1), the specimens made from GO electrical steel sheets are of different types and are subjected to different surface engineering methods. The conventional (ascribed as C\({}_{XXNY}\)) and high-magnetic-permeability (ascribed as H\({}_{XXNY}\)) GO electrical steel samples were examined during measurement. The electrical sheets came from two different manufacturers: the samples made of steel from the first manufacturer were marked as #1 and those from the second manufacturer were marked as #2. Selected steel sheets were subjected to a laser scribing procedure (ascribed as C\({}_{XXNSY}\) or H\({}_{XXLSY}\)). In addition, the sheets from manufacturer #2 were subjected to removal of the coating oxide layer (ascribed as C\({}_{27P\#2}\)) and, after removal, to the application of a nitriding process (ascribed as C\({}_{27N\#2}\)). Full details of the samples involved in the experiment and the nitriding procedures, together with metallographic tests, are described in detail in the previous article [23]. Measurements were taken with an angular resolution (\(\alpha_{\text{res}}\)) of 3.6\({}^{\circ}\), between 0\({}^{\circ}\) (TD direction of the steel) and 90\({}^{\circ}\) (RD direction of the steel) degrees, as shown in Figure 3. To perform the measurement, a system consisting of a measuring transducer, a unit for analogue signal processing, a Data Acquisition Board (DAQ) and a PC computer was used. The applied excitation signal \(U_{\text{E}}\) had a frequency of 10 Hz and a sinusoidal shape. Due to the increasing dynamics of the magnetization process with frequency, the MBN  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample Name** & **Sample Type** & **Thickness [mm]** \\ \hline C\({}_{23\text{\text{\text{\text{\text{\text{\textasciactivity identified both time and frequency increases, and so does the power spectral density increases, which cause a superposition of the periods of the high Barkhausen effect activity. However, taking into account the possibility of distinguishing these periods in time, based on preliminary tests carried out in the previous paper [25], a frequency of 10 Hz was determined for further studies, which enabled obtaining a spectrogram characteristic that highlights all the phases occurring during the magnetization of electrical sheet metal as was discussed in previous work. The magnetic field strength generated by the measuring transducer was approximately 1.6 kA/m. The Barkhausen effect can be observed in the range from 1 kHz to several hundred kHz. The filters in the analogue signal processing unit were adjusted during measurement [24]. Due to the much lower energy of the components originating from the Barkhausen effect compared to the response from the excitation field, low frequencies (within the range up to several tens of Hz) need to be filtered out from the observed band of the useful signal. Furthermore, during the analysis of magnetic anisotropy properties in electrical sheets [24], it was noted that the cutoff frequency must be adjusted to the size of the computational cell in the frequency domain resolution of the time-frequency transformation. Therefore, first, a 2 kHz high-pass filter is used to eliminate the excitation field component of the measured signal, as well as low-frequency disturbances of the measurement equipment. The upper passband range takes into account the low activity of the Barkhausen effect observed in the frequency range above 70 kHz and the Nyquist criterion and anti-aliasing filtering process related to the sampling rate (given below) as well. Thus, as a result, the signal passing to the DAQ was in the frequency range from 2 kHz to 100 kHz. The signal was read out using an NI-USB 6251 DAQ at a sampling rate of 250 kHz and stored on a PC disk managed by LabVIEW application. For one angular transducer position, 10 measurements were performed.