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.

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timevarying frequency tvf components nonstationary time series frequency content gfilter timedeformation real bat echolocation gstationary process classical linear filtering method

Krista B. Cohlmia,Wayne A. Woodward,Henry L. Gray,.G-Filtering Nonstationary Time Series. 2012 (),.

Krista B. Cohlmia,Wayne A. Woodward,Henry L. Gray,"G-Filtering Nonstationary Time Series" 2012

Krista B. Cohlmia,Wayne A. Woodward,Henry L. Gray,"G-Filtering Nonstationary Time Series"