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 Continuous wavelet transform?
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