During my internship, I've come across a software that calculates a percentage called "Index of stationarity". This index shows how much stationary is the signal. Does anyone have any idea on how to assess the stationarity of a signal?


This a very complicated question, and I would say a still open topic. The concept of stationarity is manifold, from pure statistics to applied DSP (strict, strong, wide-sense, quasi-stationarity, cyclo-stationarity, to refer to a recently closed question). The lack of access to sound models and faithful realizations renders the quest quite difficult.

Non-stationary is a non-property (like non-linearity, non-causality). Refocusing on some breeds may help its characterization, whether you are interested in:

  • randomly stepping piece-wise constant signals
  • "sines" of varying frequency (like chirps)
  • stochastic data of changing distribution
  • etc.

Yet, a common framework resides in using time-frequency representations, assuming some local stationarity and trying to assess the non-stationarity according to some metric/distance/divergence (norms, Kolmogorov, Kullback, Jensen, etc.) over the time. Here are two possible (first) references:


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