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
3 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

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: Surrogate; Spectrogram; Probability density function; Stationarity test; Time-frequency analysis

Domains: Computer Science [cs]; Signal and Image Processing; Engineering Sciences [physics]; Signal and Image processing

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⟩