Time-frequency space characterization based on statistical criterions

In this paper is proposed a method to characterize a Time-Frequency Representation (TFR). This characterization takes place in a process which aim is to extract spectral patterns of an uni-dimensional signal from its TFR. The originality of this method is that the Time-Frequency plane is considered from a local point of view. Statistical features of set of TFR coefficients are defined in order to translate this plane to a new space representation called Features Space (FS). A description of the method is proposed when the TFR is the spectrogram and the features are estimators of the first and second moments of the local sets of coefficients. Statistical properties of those features are described when the analysed signal is a white gaussian noise and when it is a deterministic signal embedded in a white gaussian noise. The obtained theoretical results allow one to discriminate in the Features Space regions of the TFR dedicated to signal spectral patterns from those dedicated to the additive noise. An example is finally presented with seismic data recording of an avalanche.