## 3 Signal Processing Techniques Applied to Wind Turbine Failure Detection
Unlike the STFT, wavelet transformation allows the window measurement to be varied in such a way that a wide window can be used when information about low frequencies is required and narrow windows when it is necessary to analyze high frequencies since the latter are detected better in the time domain, while low frequencies are more accurately analyzed in the frequency domain. This property means that wavelets can be used in the SA at different frequencies and resolutions of both stationary and transient signals [48]. \[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]1  
\[x_{\overline{t}}(m)=x(m)h(\overline{t}-m) \tag{32}\]2  
As described in reference [57], techniques such as the CWT and discrete FT have disadvantages when the analysis is carried out with small loads and close to the synchronism speed. According to this author, a more effective method for detecting faults and analyzing the evolution of their severity is to use a Kalman filter, which is computationally more efficient. Since the CWT requires considerable computational effort and generates too much data, an alternative is to filter the signal iteratively in such a way that each frequency band obtained is again decomposed and so on until we obtain several high-resolution frequency components, on which we perform the analysis. In other words, the alternative is to discretize the parameters of both scale and time, leading to the discrete wavelet transform (DWT), also called multiresolution analysis [58]. According to reference [59], calculating the coefficients throughout the scale increases the calculation time, while according to reference [60], it can be shown that the CWT is not useful for detecting faults or torque variations; therefore, the use of the DWT is preferable. According to that report, the signal must first be decomposed by the CWT with a Daubechies 8 (Db8) mother function, and then the FFT is used to analyze the spectrum components. In reference [61], the components of the fundamental frequency and harmonics due to eccentricity, slots, and other unknown causes, including environmental noise, determine the CS. However, these components are not those related to the generalized bearing roughness; therefore, to detect this type of failure, that work proposes to eliminate the mentioned components by filtering the generator stator signal from a WT using the DWT based on the coiflet function. In addition, the signal is also broken down by wavelets into several segments until the components associated with bearing failures are obtained. As described in reference [62], in regard to detecting broken bars, the main problem with steady-state analysis is that the frequency separation depends on inertia, which means that for small loads, the separation decreases to a point where the frequencies associated with the broken bars cannot be distinguished, so those authors propose processing the signal using wavelets. The current signal of an induction motor is also broken down by wavelets for the detection of broken bars under different load conditions. According to the authors, the high-order Daubechies family behaves as an ideal filter and partially avoids overlap between frequency bands. In reference [63], the current signal of an induction motor is also segmented by wavelets to detect broken bars under different load conditions. According to the authors, the high-order Daubechies family behaves as an ideal filter and partially avoids overlapping between frequency bands. According to reference [16], the use of wavelets makes it unnecessary to know the slip, and in reference [20], a diagnosis of broken bars is proposed based on the current signal and the transformation of wavelets, without using the slip. As described in reference [64], it is possible to identify the incipient presence of broken bars by applying the DWT with the Daubechies-44 family.