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Abstract:
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Many time series data sets are characterized by frequency behavior that changes with time. Examples of this type of data are Doppler signals (for measuring blood flow, etc.), heart sounds, bat echolocation signals, seismic waveforms, etc. Time series of this type are nonstationary, and the standard methods based on a stationarity assumption are not appropriate. Techniques that have been used for analyzing time varying frequency (TVF) data include wavelets and short term Fourier transforms. When the frequencies of a process are changing continuously in time, these methods may not apply. In this case a new approach based on the transformation of time may be appropriate. The strategy is to transform the time axis in order to obtain a new stationary realization that can then be analyzed by standard methods (spectral analysis, filtering, etc.).
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