## 3 MBN Signals Time-Frequency Transformation and Feature Extraction
A broader presentation of the spectrograms obtained during the research and the discussion is presented in the previous paper. Nevertheless, based on the presented exemplary distributions of \(1\,S_{\text{BN}}(t,f)\,|\,^{2}\), changes in the course of the instantaneous dynamics and the degree of activity of the MBN can be clearly noticed depending on the steel grade and machining process. Next, further processing is required. Thus, the feature extraction procedures were performed to quantify information expressed by the _TF_ spectrograms and track the changes in the analysed distributions. These features [30] refer to the description of instantaneous, as well as general, changes in the time-frequency representation. They allow for the definition of 66 features which can be divided into three major groups: describing statistical properties (such as minimum, maximum, mean, median, centroid, variance, standard deviation, skewness or kurtosis, etc. ); describing the dynamics of variance, uniformity of distribution or degree of disorder (i.e., the _TF_ distribution's shape, the energy or entropy); describing the characteristics' values referring to the symmetry, centre shift in the _TF_ plane, flatness, homogeneity or monotonicity, etc. The definitions and the properties of the used _TF_ features were discussed in previous paper by the authors [30]. Considering only the features calculated from the entire spectrogram, the vector dimension was reduced to 13 selected features. Feature extraction was performed for all spectrograms. Thus, a feature vector was obtained for each examined steel grade and each measured angular position of the transducer. Pictorially, the features can be presented using a polar chart. Such a presentation makes it possible to observe how the value of a given feature changes with the angular position of the transducer, which allows for the evaluation of the angular distribution of the magnetic properties of a given steel. Exemplary polar charts are presented in Figure 4.  
The figure shows the obtained angular characteristics of the four selected features for the single selected sample (the CGO steel after laser scribing C\({}_{27\text{LSR1}}\)). Each chart was normalized to the (0-1) range. As it can be seen, these distributions have a different shape depending on the given \(TF\) feature. Figure 4a presents the distribution of the concentration measure feature \(BN_{\text{CM}}\). As it can be seen, from 0\({}^{\circ}\) to about 75\({}^{\circ}\) there is a monotonic increase in the value, and then after reaching maximum value, a slight decrease in the value of the feature is noticeable until an angle of 90\({}^{\circ}\) is reached. The \(BN_{\text{CM}}\) feature assumes higher values for spectrograms with an even energy distribution across the entire \(TF\) plane, but at the same time it is not sensitive to small values. Therefore, as the level of MBN activity increases throughout the spectral band while approaching the vicinity of the easy magnetization axis, this feature also takes higher values. Figure 4b presents the distribution of the spectral entropy feature \(BN_{\text{SE}}\). The value of this feature in the angular interval between 0\({}^{\circ}\) and 60\({}^{\circ}\) maintains almost a constant close to 1, while for angle between 60\({}^{\circ}\) and 90\({}^{\circ}\), there is a sharp decrease in the value to 0. Because \(BN_{\text{SE}}\) can assess the degree of disorder in a distribution, when the feature reaches values close to 0 for the direction close to the axis of easy magnetization, it can be interpreted as leading the distribution to attain a higher degree of order and to accommodate the existing energy states. Figure 4c shows the coefficient of variation \(BN_{\text{CoV}}\) feature. The value increases from 0\({}^{\circ}\) to about a 90\({}^{\circ}\) angle, where at about 90\({}^{\circ}\) it obtains the highest value.