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Signals made of the superimposition of a reduced number of AM-FM components can be characterized by a time-frequency signature which consists of weighted trajectories in the plane, thus ending up with an ideal representation of their energy distribution that is intrinsically sparse. Elaborating on first studies that pioneered a compressed sensing solution to the question of approaching such an ideally...
A method is proposed for testing stationarity in an operational sense, i.e., by both including explicitly an observation scale in the definition and elaborating a stationarized reference so as to reject the null hypothesis of stationarity with a controlled level of statistical significance. While the approach is classically based on comparing local vs. global features in the time-frequency plane,...
Recently, a time-frequency approach for testing stationarity was proposed. However, this method inefficiently detects nonstationarities of the first-order. Here, we present two contributions that improve the test performance and allow the detection of first-order evolutions. The first one is to use an adequate distance measure. The second is a modification of the method in order to consider the spectral...
An operational framework is developed for testing stationarity relatively to an observation scale. The proposed method makes use of a family of stationary surrogates for defining the null hypothesis of stationarity. As a further contribution to the field, we demonstrate the strict-sense stationarity of surrogate signals and we exploit this property to derive the asymptotic distributions of their spectrogram...
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