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I have a signal

$$Y=f(t),$$

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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  • $\begingroup$ Complex topic, this might help (includes learning references). $\endgroup$ Mar 28 at 19:43
  • $\begingroup$ A huge topic. Describing the anomalies with respect to the "normal" behavior could help us. Basically, if the signal is 1D, and you don't have too much computational constraints, doing CWT to understand, before going to the more economical DWT, is generally advised $\endgroup$ Mar 29 at 13:46
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    $\begingroup$ @LaurentDuval thank you for your response. $\endgroup$
    – nacertrez
    Apr 2 at 14:25
  • $\begingroup$ @OverLordGoldDragon thank you for your response. $\endgroup$
    – nacertrez
    Apr 2 at 14:25
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    $\begingroup$ @LaurentDuval je pense que vous maitrisez mieux le traitement de signal. si oui puis-je vous contacterez en privé? $\endgroup$
    – nacertrez
    Apr 2 at 14:28
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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).

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