Using Time Deformation to Filter Nonstationary Time Series with Multiple Time-Frequency Structures

For nonstationary time series consisting of multiple time-varying frequency (TVF) components where the frequency of components overlaps in time, classical linear filters fail to extract components. The G-filter based on time deformation has been developed to extract components of multicomponent G-stationary processes. In this paper, we explore the wide application of the G-filter for filtering different types of nonstationary processes with multiple time-frequency structure. Simulation examples illustrate that the G-filter can be applied to filter a broad range of multicomponent nonstationary process where TVF components may in fact overlap in time.