A non-stationary index resulting from time and frequency domains

Detecting the presence of non-stationarity events in a signal is a challenge that is still not taken up. The aim of this paper is to make a contribution to this key issue. We already proposed a non-stationarity detection defined in time-frequency domain in order to control the invariance of the time-frequency statistics. In this paper, in order to be not limited by the time and frequency resolution of a time-frequency approach, we propose another test in frequency domain. In frequency domain, the problem can be cast by taking advantage of the normalized-variance properties of a spectral estimator when analyzing non-stationary signals. This second test will confirm, invalidate or detect new frequency localizations of non-stationarities. Finally, the main contribution of the paper is to propose a stationary index defined so as to merge the information given by these two tests and to allow an alarm to be raised for a high level of non-stationarities. Applications on real-world signals show the pertinence of this new index.