## 3 MBN Signals Time-Frequency Transformation and Feature Extraction  
Further, the MBN _TF_ representations \(S_{\text{BN}}(t,f)\) were expressed in the form of spectrograms \(\mid\)\(S_{\text{BN}}(t,f)\)\(\mid\)\({}^{2}\). Figure 3 shows the exemplary spectrograms, obtained for MBN signals acquired for four different samples and the orientation of the transducer along the RD (90\({}^{\circ}\)): the CGO steel sample with thickness of 0.23 mm (C\({}_{23\#1}\)), the CGO steel sample with thickness of 0.27 mm after decoating of the oxide layer (C\({}_{27\#2}\)), the CGO steel sample with thickness of 0.27 mm after nitriding process (C\({}_{27\text{N}\#2}\)) and the HGO steel sample after laser scribing (H\({}_{23\text{L}\#1}\)). The results were presented in common range and colour map was expressed in linear scale. In the case of the CGO C\({}_{23\#1}\) sample (Figure 3a), there are two clearly visible areas of increased activity. The first is in the vicinity of 0.02 s, and the next is in the subperiod from about 0.03 to about 0.04 s. Figure 3b shows a spectrogram achieved for the laser scribed HGO H\({}_{23\text{L}\#1}\). In this case, on the obtained _TF_ characteristics, three clearly distinguished areas of activity can be noted, which also cover a much wider time segment of the magnetic field half-period than in the previous cases. Figure 3c shows the spectrogram obtained for CGO sample C\({}_{27\#2}\) subjected to decoating of the oxide layer. As it can be seen, the presented characteristic of activity in the _TF_ space is similar to that presented in Figure 3a  
Figure 3: Exemplary _TF_ spectrograms obtained for alignment of the transducer along the rolling direction RD for four different test samples: (**a**) CGO steel sample with thickness of 0.23 mm (C\({}_{23\#1}\)), (**b**) high GO steel sample after laser scribing (H\({}_{23\text{L}\#1}\)) (**c**) CGO steel sample with thickness of 0.27 mm after decoating of the oxide layer (C\({}_{27\#2}\)) and (**d**) CGO steel sample with thickness of 0.27 mm after nitriding process (C\({}_{27\text{N}\#2}\)). in the sense that it also shows two distinguished areas of activity. Nevertheless, in this case, the areas of this activity cover a smaller space of the _TF_ distribution, which is especially noticeable in the case of the second activity area. In addition, the amplitudes over the spectrogram, in general, take lower values (it should be emphasized that both sheets come from different manufacturers thus are characterized by a different value of magnetic permeability and have different thickness as well, which affects the differences in received power density levels). In general, at least the three key phases of the magnetization process can be distinguished for GO steels (visible especially when magnetization direction is close to the easy magnetization axis): the first is related to the reversed domain nucleation process bonded with the magnetocrystalline anisotropy, while the second is related to the movement of the 180\({}^{\circ}\) domains occurring close to the main MBN peak, and the third is related to the movement of the 90\({}^{\circ}\) domains [22]. While in the case of HGO three areas that may refer to the described magnetization phases are clearly visible, in the other two cases (Figure 3a,c) they may be hidden. In the case of C\({}_{2381}\), the first visible activity subperiod is relatively compact in time while the second one is more stretched. This may indicate the overlapping of the subperiods of the second and third magnetization phases in that situation. Similarly, in the case of C\({}_{277\text{PfB}}\), around 0.04 s, one more area with a much lower level of value can be noticed. Figure 3d shows the spectrogram of nitrided CGO steel which was first subjected to the oxide layer decoating process. This spectrogram is characterized by only a single, but wide, area of activity, which proves the significant influence of nitriding on the original structure of the material.