A nonparametric test for stationarity based on local Fourier analysis

Authors:
Prabahan Basu;Daniel Rudoy;Patrick J. Wolfe
Affiliations:
Statistics and Information Sciences Laboratory, Harvard Engineering and Applied Sciences, 33 Oxford Street, Cambridge, MA 02138 USA;Statistics and Information Sciences Laboratory, Harvard Engineering and Applied Sciences, 33 Oxford Street, Cambridge, MA 02138 USA;Statistics and Information Sciences Laboratory, Harvard Engineering and Applied Sciences, 33 Oxford Street, Cambridge, MA 02138 USA
Venue:
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Year:
2009

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Abstract

In this paper we propose a nonparametric hypothesis test for stationarity based on local Fourier analysis. We employ a test statistic that measures the variation of time-localized estimates of the power spectral density of an observed random process. For the case of a white Gaussian noise process, we characterize the asymptotic distribution of this statistic under the null hypothesis of stationarity, and use it to directly set test thresholds corresponding to constant false alarm rates. For other cases, we introduce a simple procedure to simulate from the null distribution of interest. After validating the procedure on synthetic examples, we demonstrate one potential use for the test as a method of obtaining a signal-adaptive means of local Fourier analysis and corresponding signal enhancement scheme.