## 5 Results and Discussion
Although there is considerable similarity in the spectrum of the three phases obtained with this technique, differences in the composition of the spectrum and the magnitude of the components can also be highlighted, providing another indication of failure. Figure 3: PSD applying [PERSON]’s periodogram. (**a**) Phase A and (**b**) three phases. As we have been able to verify from the techniques used so far, time-domain analysis does not provide the frequency spectrum, while the analysis in the frequency domain does not provide the moment at which the components are produced. By applying the algorithm of reference [94] to calculate the STFT in MATLAB, Figure 5 is obtained. Parts a and b of this figure emphasize how both the fundamental frequency and its components, which remain invariant over time, stand out in terms of their energy (yellow color). Part b reveals harmonics very close to the fundamental (green and orange color), which correspond to the frequencies of 10 and 5 Hz mentioned above. Figure 4: Signal cepstrum of the electric generator. Figure 5: Amplitude spectrogram of the SCG. (**a**) 2 dimensional STFT, (**b**) 3 dimensional STFT. From a conceptual point of view, the STFT is one of the most important techniques and serves as the basis for other signal processing techniques. However, its main disadvantage is that it uses the same window width for the entire signal, resulting in the resolution in the time and frequency domain being constant and only one frequency band being known. If the window is wide, a good resolution is obtained in time, but a poor resolution is obtained in the frequency domain, whereas when the window is narrow, the opposite occurs. Therefore, if the frequency components are well separated, a good resolution over time may be preferred, whereas when the components are close together, the frequency resolution is prioritized. The STFT is suitable for the analysis of quasistationary signals (stationary at the window scale), which do not precisely represent the behavior of real signals. Another disadvantage is that there are no orthogonal bases for the STFT, so it is difficult to find a quick and effective algorithm to calculate it [45; 65]. According to reference [47], the STFT is positive in all parts and fulfills the positivity requirement, but regardless of the selected window, it does not provide adequate resolution to distinguish the components, nor does it manage to show the instantaneous frequency that can be obtained by the WVD. However, the WVD does not meet the positivity, global average, and finite support requirements. As described in reference [38], one of the main disadvantages of bilinear distributions, such as the WVD, is the interference terms formed by the transformation, which makes interpretation difficult and prevents identifying the true components. To correct this disadvantage, distributions such as the Choi-Williams distribution, pseudo-Wigner-Ville distribution (PWVD), and smooth pseudo-Wigner-Ville distribution (SPWVD) are used [95]. Applying the SPWVD to the WT signal under study, Figure 6 is obtained. The 50 Hz frequency (yellow color) and its harmonics stand out, and--as with the previous techniques--components including 5 Hz can be distinguished along with the fundamental wave. Despite this advantage, in Figures 5 and 6, the disadvantages of the STFT and WVD mentioned by references [38; 47] can respectively be seen. According to reference [96], when the carrier signal frequency is on the order of kHz, bearing failures cannot be detected. However, by applying envelope analysis at the lower frequencies, detection is possible. This is the foundation on which techniques such as the shock pulse meter (SPM) and spike energy are based. HT demodulation, either directly to the current signal or to the Park transformation, is used to detect various types of rotor and stator faults, such as broken bars and inter-turn short circuits.