Statistical hypothesis testing with time-frequency surrogates to check signal stationarity

International audienceAn 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 and power spectral density. A statistical hypothesis testing framework is then proposed to check signal stationarity. Finally, some results are shown on a typical model of signals that can be thought of as stationary or nonstationary, depending on the observation scale used

Testing Stationarity with Time-Frequency Surrogates

International audienceA 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, the test operates with a family of stationarized surrogates whose analysis allows for a characterization of the null hypothesis. The general principle of the method is outlined, practical issues related to its actual implementation are discussed and a typical example is provided for illustrating the approach and supporting its effectiveness

Testing Stationarity with Surrogates: A Time-Frequency Approach

International audienceAn operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local time-frequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests. The first one makes use of suitably chosen distances between local and global spectra, whereas the second one is implemented as a one-class classifier, the time-frequency features extracted from the surrogates being interpreted as a learning set for stationarity. The principle of the method and of its two variations is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used

Distribution temps-fréquence à noyau radialement Gaussien : optimisation pour la classification par le critère d'alignement noyau-cible

Cet article traite de l'ajustement des paramètres des distributions temps-fréquence pour la résolution d'un problème de classification de signaux. On s'intéresse en particulier à la distribution à noyau radialement Gaussien. On exploite le critère d'alignement noyau-cible, développé pour la sélection du noyau reproduisant dans le cadre des méthodes à noyau. Celui-ci présente l'intérêt de ne nécessiter aucun apprentissage de la statistique de décision. On adapte le critère d'alignement noyau-cible au noyau radialement Gaussien, en détournant une technique classique de réduction de termes interférentiels dans les représentations temps-fréquence. On illustre cette approche par des expérimentations de classification de signaux non-stationnaires

Time-Frequency Learning Machines

International audienceOver the last decade, the theory of reproducing kernels has made a major breakthrough in the field of pattern recognition. It has led to new algorithms, with improved performance and lower computational cost, for non-linear analysis in high dimensional feature spaces. Our paper is a further contribution which extends the framework of the so-called kernel learning machines to time-frequency analysis, showing that some specific reproducing kernels allow these algorithms to operate in the time-frequency domain. This link offers new perspectives in the field of non-stationary signal analysis, which can benefit from the developments of pattern recognition and Statistical Learning Theory

Time-Frequency Learning Machines For NonStationarity Detection Using Surrogates

International audienceTesting stationarity is an important issue in signal analysis and classification. Recently, time-frequency analysis has been investigated to detect the nonstationarity of a given signal, by constructiing from it a set of surrogate, stationarized signals. Time-frequency features are extracted to test the stationarity. Our paper is a further contribution by exploring the powerful framework of time-frequency learning machines. We show that one can relate stationarity to the structure of surrogates spectrograms and detect nonstationarity using a one-class classification approach. The proposed method does not suffer from any prior knowledge for extracting features, since it uses the entire time-frequency information. Using spherical multidimensional scaling technique, we illustrate the relevance of the proposed approach with simulation results

Time-Frequency Learning Machines For NonStationarity Detection Using Surrogates

International audienceTesting stationarity is an important issue in signal analysis and classification. Recently, time-frequency analysis has been investigated to detect the nonstationarity of a given signal, by constructiing from it a set of surrogate, stationarized signals. Time-frequency features are extracted to test the stationarity. Our paper is a further contribution by exploring the powerful framework of time-frequency learning machines. We show that one can relate stationarity to the structure of surrogates spectrograms and detect nonstationarity using a one-class classification approach. The proposed method does not suffer from any prior knowledge for extracting features, since it uses the entire time-frequency information. Using spherical multidimensional scaling technique, we illustrate the relevance of the proposed approach with simulation results