"APPLICATIONS OF THE HILBERT-HUANG TRANSFORM"
A new method, the Hilbert-Huang Transform, has been developed
for analyzing nonlinear and nonstationary data. The key part of the
method is the Empirical Mode Decomposition 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 extrema, and also having symmetric
envelopes defined by
the local maxima and minima respectiely. The IMF also
admits well-behaved Hilbert transform. This ecomposition 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 nonlinear and nonstationary 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. With this technique we can examine
the detailed dynamics characteristics of a nonlinear system through the
instantaneous frequency rather than harmonics. Thus it constitutes a new
view of the nonlinear dynamics. Examples of classic nonlinear equations
and other nonlinear and nonstationary data sets will be used as examples
to illustrate the advantage of the application of this new data analysis
method.