I have a signal
which I want to show the anomalies, using the wavelets transform.
I don't know if I use the CWT or the DWT and which mother wavelet could I use?
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You want to display anomalies in a continuous time signal. Anomalies are generally defined with respect to some thought normality. Wavelets are great tools to detect singularities (jumps, non-smooth derivatives) in otherwise regular data. They can perform other tasks, and they were proven especially efficient on piece-wise polynomial signals with discontinuities.
If you first want to identify or detect the defects, and you are not restrained by computational power or real-time needs, time-scale or time-frequency transforms are a good starting point. So, CWT is a great tool.
Yet, it is redundant, etc. So when you actually know what you are looking for, you can choose your best wavelet, and turn to a more efficient approximate version using for instance the discrete wavelet transform (DWT).