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Continuous wavelet transformation has been quite widely used for various applications. Most of the papers that I found were using CWT for non-stationary signals. Can we use CWT for stationary signal analysis? if not what are the drawbacks in using Continous wavelet transform?

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  • $\begingroup$ The signal I'm analyzing is a very short peaky signal. I did test the signal to measure it's stationary using two ways. First one is the sliding window method where I found that statistics of the signal changes in each window. This indicates that the signal is non-stationary. but when I tried the dickey fuller test it showed me that the signal is stationary. I'm confused about which one I should really on? $\endgroup$ – hasi Jun 17 '19 at 22:47
  • $\begingroup$ is there any way that I can directly contact you? $\endgroup$ – hasi Jun 17 '19 at 23:11
  • $\begingroup$ Any more details needed? $\endgroup$ – Laurent Duval Oct 28 '19 at 21:04
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Stationarity is a multi-fold concept in signal processing. It can denote a wide range of behavior, encompassing deterministic or stochastic aspects. Beyond that, the main question is: do you know if your signal is stationary, and how?

If you actually know how, it is probably wiser to use the generation process to build a custom, adapted model or transformation, and use it for the analysis.

Even in that case, I strongly advocate using different analysis methods in parallel, to help you detect artifacts, issues than you would not detect with a single model. For instance, let us remind that one usually observe only a few realizations of a "signal", and that acquisition issues, outliers, etc. may occur.

Finally, analyzing in first intention a signal with time-frequency or time-scale transforms is a good idea, as it can help you detect the useful scales of interest, estimate parameters of stochastic events, etc.

The drawbacks are:

  • The difficulties in choosing the appropriate wavelet (real or complex), and the associated sampling (and the resulting speed)
  • The difficulties in interpreting the scalogram, as a knowledge of the underlying processes could be useful
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