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

Cédric Richard 1 André Ferrari 1 Hassan Amoud 2 Paul Honeine 2 Patrick Flandrin 3 Pierre Borgnat 3
1 FIZEAU - Laboratoire Hippolyte Fizeau
2 LM2S - Laboratoire Modélisation et Sûreté des Systèmes
ICD - Institut Charles Delaunay
3 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
Abstract : 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 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.
Keywords : Probability density function Time-frequency analysis Stationarity test Surrogate Spectrogram
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Conference papers
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Cédric Richard, André Ferrari, Hassan Amoud, Paul Honeine, Patrick Flandrin, et al.. Statistical hypothesis testing with time-frequency surrogates to check signal stationarity. IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP-10, Mar 2010, Dallas, United States. pp.3666-3669, ⟨10.1109/ICASSP.2010.5495887⟩. ⟨ensl-00476017⟩

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