Time variation characterization of a nonstationary time series

Abstract

The Fourier transform of a nonstationary time series has the difficulty of providing a proper physical interpretation of the signal as the physical attributes and dynamics associated with the time series may consist of several transients that are different in their nature. The time series analysis method developed by NASA [N. Huang et al., ‘‘The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis’’ (to be published)] has a unique approach to adaptively break down the nonstationary time series into the sum of several simple mode functions. Each single mode function can then be expressed in terms of an analytical signal whose amplitude and phase can both be varied with time. Those time variations can be related to the abrupt changes associated with dynamic systems. Such a time variation characteristic can be used to observe the occurrence of a transient event even in a nonstationary process. Applications of this technique to observe various types of acoustic signals in noisy environments are discussed.