A New Method for Non-linear and Non-stationary Time Series Analysis: <br/>The Hilbert Spectral Analysis

About

A new method for analysing non-linear and non-stationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero crossing and extreme, and also having symmetric envelopes defined by the local maximal and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Classical non-linear system models are used to illustrate the roles played by the non-linear and non-stationary effects in the energy-frequency-time distribution. Examples including Duffy equation, Rossler Equation, and non-linear wind wave data will be discussed to show the new Hilbert view of non-linear and non-stationary systems.

Organiser(s): Luigi Di Lella / EP Division

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