## 4 Vibroarthrography of the Knee Joint
### Feature Extraction and Classification
#### 4.3.1 Feature Extraction and Selection
The Mann-Whitney U test was used with a continuity correction for discriminants without a normal distribution. On this basis, seven discriminants with significant statistical differences between the analysed groups were selected and used as input data in the subsequent classification. These included SA, RMS, VAR, PV, PPC, CF, and K.  
Similar features were also included by [PERSON] et al. in their work [121]. In addition to PPV, AE, VAR, MF, K, S, and FF, they also included the impulse index (II), the purpose of which is to detect statistical parameters of the presence of shocks in the VAG signal. Further time domain features, such as M6A and M8A, were included in the works of [PERSON] et al. [76; 77]. The M6A parameter can be described as the sixth central moment. Higher central moments may indicate skewness and kurtosis of the signal. In turn, the M8A parameter is the eighth central moment whose higher values enable a more accurate description of the signal nonlinearity and its extreme values. The frequency domain is more complex than the time domain. Its purpose is to explore the frequency content of the VAG signal. Fourier transform (FT) is widely used to convert a signal from the time domain to the frequency domain [123; 124]. However, this method seems to be insufficient due to the nonstationary nature of VAG signals. [PERSON] et al. [87] included the FM4 parameter in the frequency domain. FM4 can be described as the kurtosis of the differential signal. It is used in the analysis of complex dynamic phenomena. FM4 characterises the amplitude of the differential signal. Time-frequency domain analysis uses techniques such as short-time Fourier transform (STFT), wavelet transform (WT), and Wigner Ville distribution. STFT extends the classical Fourier transform to analyse nonstandard signals whose characteristics change over time. Its purpose is to divide the signal into short time segments for which a standard Fourier transform is performed [131]. Wavelet transform is a signal analysis technique that offers variable time-frequency resolution, in contrast to STFT. Functions called wavelets are scaled and shifted in time, making it possible to analyse signals with different scales and frequencies [132]. [PERSON] et al. [88] used wavelet packet transform (WPT) for feature extraction. WPT is an extension of wavelet transform (WT) whose task is to decompose the signal into sub-bands of different frequency and time resolutions. Feature extraction was performed for each distributed wavelet coefficient. Statistical parameters such as skewness and kurtosis were used as features. The use of WPT generates a multidimensional feature vector, which makes it possible to obtain more information about the signal. Unfortunately, this is associated with an increase in the values of the pattern classifier learning parameters and computational complexity. For this reason, the principal component analysis (PCA) method was used to reduce the features. From the total number of 60 features extracted from the decomposed signal, their number was reduced to 26 for SW movement and 27 for SSS movement using PCA. For feature extraction in the time-frequency domain, [PERSON] et al. [92; 104] used continuous wavelet transform (CWT). At high frequencies CWT analysis is performed to observe the frequency response of the reconstructed signal. CWT tends to provide good time resolution and relatively poor frequency resolution, while at low frequencies, it provides good frequency resolution and relatively poor time resolution [133]. Continuous wavelet transform peak values were obtained in all flexion and extension frequency ranges. In healthy individuals, a higher value of the coefficient was noted in the low-frequency band, while in individuals diagnosed with knee osteoarthritis, the value was higher in the high-frequency band. In their work, [PERSON] et al.