Constructing adaptive interference-reduced Wigner-Ville spectral estimators of non-stationary time series
Seminar Room 1, Newton Institute
AbstractCo-authors: Florent Autin (Université d'Aix-Marseille 1), Gerda Claeskens (KULeuven), Rainer von Sachs (UCLouvain)
In this talk we propose estimators of the time-frequency spectrum of a (zero mean) non-stationary time series with second order structure which varies across time. It is obtained by smoothing the empirical Wigner-Ville (WV) spectrum (Martin and Flandrin, 1985) which is a highly localized time-frequency spectrum. Using the empirical WV avoids prior time-frequency segmentation (such as for the segmented periodogram (Schneider and von Sachs, 1996)) nevertheless it suffers from low and heterogeneous signal-to-noise ratios and from severe interferences. In addition, the associated time-frequency spectrum is best modeled as an anisotropic object with locally varying smoothness in both time and frequency directions (Neumann and von Sachs, 1997). All this make smoothing very challenging. Our approach is to project the empirical WV data onto a specifically designed hyperbolic wavelet basis (Autin et al, 2013) and to use a tree-structured thresholding (Autin et al, 2011, 2013) under co nstraints inspired notably by the Heisenberg's uncertainty principle. Such approach is expected to ensure an adaptive time-frequency representation and to reduce the cross-interferences of the WV spectrum.