An operational framework is developed for testing stationarity of any signal relatively to an observation scale. The originality is to extract time-frequency features from a set of stationarized surrogate signals, and to use them for defining the null hypothesis of stationarity.

The surrogate data technique generates a family of stationarized signals, by destroying the time-varying structures in the signal phase while keeping its spectrum unchanged. In practice, this is achieved by keeping unchanged the magnitude of X(f), the Fourier transform of the initial signal x(t), and replacing its phase by a i.i.d. one. This leads to as many stationary surrogate signals as phase randomizations are operated.

The originality is to make use of the family of stationary surrogate signals for defining the null hypothesis of stationarity and, based upon this information, to derive statistical tests. Many contributions have been proposed, mainly by the use of machine learning.

# Some Related Papers

P. BORGNAT, P. Flandrin, P. HONEINE, C. RICHARD, and J. XIAO**Testing Stationarity with Surrogates: A Time-Frequency Approach***IEEE Trans. on Signal Processing*, 58 (7) : 3459–3470, July 2010.

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C. RICHARD, A. FERRARI, H. AMOUD, P. HONEINE, P. FLANDRIN, and P. BORGNAT**Statistical hypothesis testing with time-frequency surrogates to check signal stationarity***Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*, Dallas (Texas), 14 – 19 March, 2010.

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H. AMOUD, P. HONEINE, C. RICHARD, P. BORGNAT, and P. FLANDRIN**Time-Frequency Learning Machines For Nonstationarity Detection Using Surrogates***Proc. of IEEE Statistical Signal Processing Workshop (SSP)*, Cardiff (Wales), UK, 31 Aug. – 3 Sept., 2009.

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H. AMOUD, C. RICHARD, P. HONEINE, P. FLANDRIN, et P. BORGNAT**Sur la caractérisation de non-stationnarités par la méthode des substituts**

Actes du *22-ème colloque GRETSI : Traitement du signal et des images*, Dijon, France, 8 – 11 Sept. 2009.

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