G-filtering nonstationary time series

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time,and those nonstationary time series with time-varying frequency (tvf) components that do not overlap. however,for many types of nonstationary time series,the tvf components often overlap in time. in such a situation,the classical linear filtering method fails to extract components from the original process. in this paper,we introduce and theoretically develop the g-filter based on a time-deformation technique. simulation examples and a real bat echolocation example illustrate that the g-filter can successfully filter a g-stationary process whose tvf components overlap with time. copyright © 2012 mengyuan xu et al.