## 2 Literature Review
### Continuous Wavelet Transform (CWT)  
Wavelet transform gives a good time-frequency representation in the processing of non-stationary signals. With the dilation and translation of the mother wavelet [17], wavelet transform can capture the time and frequency information of a given signal. [PERSON] et al. [18] reviewed the application of continuous wavelet transform (CWT) in the analysis of vibration data. They used the Gabor wavelet as the mother transform function. They demonstrated selection of parameters and supported new extensions of the wavelet transform method to overcome drawbacks while balancing time-frequency resolution trade-off. The Gabor wavelet was applied as a sliding window function to create short time Fourier transform (STFT) by the integration of the inner product of the sliding window function. The spectrogram, which was the squared absolute value of the STFT, could then be computed as indicators of faults in applications such as machinery monitoring [19] and acoustic localization of aircraft [20]. However, the fixed sliding window size has the possibility of losing high frequency information during signal analysis due to the fixed time and frequency information. Additionally, STFT is only suitable for stationary signal analysis, while most of the signal types in the manufacturing process are non-stationary. An alternative signal processing method is needed. [PERSON] et al. [21] developed a new demodulation analysis using Hilbert transform based on a time-frequency method known as empirical model decomposition. The new analysis method was applied to analyse the gearbox of a wind turbine with gear-pitting fault. Theywere able to extract the fault modulation information without human intervention and with more exact information. Their work indicated that the readability of the CWT scalogram could be improved by the selection of different types of wavelets and noise interferences introduced in the system. A CWT scalogram reflects the energy density of signals. Abrupt transition in signals result in a larger absolute value of the coefficient, which usually represents brighter colours in the scalograms. This is often used as the observation reference of the singular frequencies [22]. In the traditional CWT scalogram analysis, fault features are detected by CWT, the whole data set, and by observing the colour in the scalograms [23]. The readability of the CWT scalogram can be affected by the selection of different types of wavelets and noise interferences in the experiment. [PERSON] et al. [24] had a different opinion of the selection of waveforms in mechanical signal analysis. They justify their idea by comparing the performance of Haar CWT transform with Morlet CWT transform. They claim that Haar CWT transform has a better performance on the fault detection of gear crack and ball bearing. The result broadens the way of thinking about how to select the suitable wavelets, since the similarity between the wavelet and signal is not the only criterion. A CWT scalogram can be combined with a method such as empirical mode decomposition to predict respiratory disorders [25], detect faults in turbine gearbox [26], and monitor rolling bearing faults [27]. Furthermore, a CWT transform can be utilised as a feature extraction method to integrate with deep learning algorithms and build a system that can autonomously identify the fault at its incipient stage. [PERSON] et al. [28] applied CWT as a tool to convert the scalogram to grey-scale images and then apply an adaptive CNN (convolutional neutral network) to identify the pump condition. [PERSON] et al. [29] developed a four-step method to identify weak fault information. Step 1 was to process multi-cycle signals with CWT. Step 2 was to obtain the corresponding scalogram, which was then analysed in Step 3 by reassigned wavelet transform. Finally, synchronous averaging was applied to the signals for every working cycle of the bearing in Step 4. The proposed method was found effective.