A criterion for detecting nonstationary events

Nadine Martin (1)

1 LIS - Laboratoire des images et des signaux

This paper tackles the problem of detecting nonstationary events in a signal. An ergodic process is stationary if its law is invariant whatever the time translation is. So the control of the invariance of the law parameters can lead to a stationarity measure. We propose such a test stated from a time-frequency representation so as to localize both in time and frequency nonstationary events. At each frequency we define two observation subsets. The first one is the subset of time frequency points, whose process is random and stationary eventually added with a deterministic process. The second one gathers all time-frequency points, whose process is non stationary. The problem is thus simplified into two competing sets or hypotheses between which we have to choice. A binary hypothesis test is stated from the Neyman-Pearson criterion. We construct a decision rule to have maximum probability of detection while not allowing the probability of false alarm to exceed a given value. Given that no a priori information is known, a recursive algorithm is performed in order to estimate the unknown parameters of the decision rule. The test converges when the subsets become steady. To be independent of the choice of the false alarm probability, the decision rule is applied for different values of this probability. To initialize the algorithm, we only assume that a time stationary part exists at each frequency. Under all these assumptions, all types of nonstationarities can be detected. The proposed detector is a post-processing to a timefrequency estimator. In this paper, we use a spectrogram or a gliding correlogram, which sets the size of the nonstationary events to detect. The detector could be adapted to any other time-frequency estimator if its statistical law is known. Applications on real signals are carried out and show that the proposed method performs well.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Nadine Martin. A criterion for detecting nonstationary events. Twelfth International Congress on Sound and Vibration, ICSV12, Jul 2005, Lisbon, Portugal. ⟨hal-00370106⟩