## 3 Wavelet Analysis for Gerbox Diagnostics  
As previously stated, the wavelet coefficients contain information about vibration amplitude in the time-frequency domain. Many studies use wavelet coefficients derived from CWT, DWT, or WPT computations, which are then integrated with other mathematical and statistical analysis approaches to provide signal analysis tools for gearbox diagnostics in non-stationary conditions. [PERSON] [36] and colleagues used the independent component analysis (ICA) approach using wavelet coefficients to monitor and diagnose tooth faults in gears using a single vibration sensor. To obtain characteristic values for gearbox faults, [PERSON] and [PERSON] [37] approximated the wavelet coefficients as simple sine functions to estimate the autocorrelation function. The method of frequency averaging is applied in the time-frequency domain to detect the presence and progression of tooth surface pitting, as indicated in [38]. In [39], wavelet coefficients are utilized to quantitatively assess the severity of tooth fault under varying load conditions. Researchers used the CWT to extract various statistical parameters, such as standard deviation and kurtosis coefficient, from the wavelet coefficients of vibration data. This analysis employed multiple base wavelet functions to detect faults in gears and rolling bearings [40; 41; 42]. [PERSON] and colleagues [43] used the Hermitian basis wavelet function to perform CWT in order to detect common local faults in gearboxes, such as teeth cracks and chipped gear peaks. Furthermore, the amplitude and phase values of CWT using the Hermitian wavelet function are also employed simultaneously to identify faults in the rolling bearings in the gearbox [44; 45; 46]. By using the low-pass filtering characteristics of the Haar wavelet function, [PERSON] et al. [43] used the CWT to identify the low-frequency regions, which are symptoms of gears and rolling bearings faults. [PERSON] et al. [47; 48; 49; 50] presented a technique for assessing the correlation among wavelet coefficients of measured signals to detect several types of localized faults in gearboxes. [PERSON] [51] and colleagues analyzed gearbox vibration using DWT and CWT to investigate the correlation between the wavelet coefficient and the distribution of faults on the gear. [PERSON] et al., applied CWT and DWT with optimized parameters combined with autocorrelation functions to diagnose faults in industrial gearboxes [52]. Researchers also employed wavelet analysis as an efficient preprocessing method to enhance the quality of diagnostic information in signals and reduce noise. [PERSON] and [PERSON] et al., diagnosed the rolling bearing fault in the gearbox using the noise-reduced signal's autocorrelation function, which was processed with CWT [53; 54]. [PERSON] and colleagues have combined the noise removal method through time-domain averaging with the Morlet wavelet \"filter\" to diagnose tooth faults in gears from measured raw signals [55]. [PERSON] and colleagues [56] have developed a method for simultaneously detecting multiple faults on gears using DWT combined with Principal Component Analysis (PCA). In this method, DWT is employed as a signal-preprocessing tool. [PERSON] [57], [PERSON] [58], and [PERSON] [59] proposed highly effective denoising solutions based on CWT and DWT to detect weak periodic pulse signals caused by tooth meshing impact. The wavelet analysis outputs from the recorded vibration signal during gearbox operation can also be used as input for intelligent monitoring and diagnostic systems, including genetic algorithms, neural networks, or support vector machine classifiers (SVM). Notably,a signal analysis system based on CWT with Morlet wavelet and genetic algorithm is proposed to automatically detect rolling bearing and gear faults from vibration signals [60; 61; 62]. [PERSON] and colleagues [63] derived statistical indicators using the wavelet coefficient to automatically detect and classify faults in rolling bearings using neural networks.