HHT MATLAB Software
Introduction
The Hilbert-Huang transform (HHT) has attracted increasing attention in scientific and engineering
communities ever since its introduction (Huang et al. 1998, Huang et al. 1999). And the core of HHT, the
Empirical Mode Decomposition (EMD), has also won wide acceptance. However, due to sensitivities of the EMD
outputs to the selections of different parameters (such as a stoppage criterion) or processes (such as an
end-point approach) in the original EMD algorithm, the use of EMD has caused some confusion. Efforts were
made to ameliorate the confusion by eliminating mode mixing (Huang et al., 1999), adding confidence limit
to the results (Huang et al., 2004). Those efforts were successful only partially. Anxiety to many users
of EMD remains, especially on the interpretations of the EMD outputs. An optimized EMD program would undoubtedly
be the goal, and may be the Holy Grail, we are trying to get.
From a theoretical consideration, we anticipate the HHT method to remain an empirical one for the foreseeable
future. In other word, we can improve the operational efficiency and robustness; we can also make incremental
progresses on the theoretical foundation of the adaptive data analysis approach, but the existing mathematical
problems listed by Huang (2005) would present daunting challenges to the mathematical community for a long
time. The most difficult part of the challenge is to establish a general adaptive decomposition approach
of analysis without
a priori
basis. We believe this challenge would most likely remain as an open one for
the longest time. The situation is not unlike the progress of most inventions in mathematics and
sciences. Take calculus or Fourier Transform as examples: As we know, initially calculus was just treated
as an algorithm. It was rigorously established only after the introduction of the concept of limit; while,
Fourier transform would have to wait till measure theory was invented. We have to wait too.
Mathematical problem notwithstanding, over the past few years, the HHT method has been applied to a wide
range of problems with great success. Up to this time, most of the progresses in HHT are in the application
areas. The state-of-the-arts of HHT are at this stage corresponding historically to the wavelet analysis
in the earlier 1980s: producing great results but waiting for mathematical foundations to make the method
more rigorous and robust. Some of the recent developments especially the Ensemble EMD given below had
substantially removed most of the practical anxieties.
To promote openness in scientific exchanges and enhance the progress of HHT, we decided to post our MatLab
codes at this Website. We hope the users would try and advise us of potential problems, so that we could
work together to push the HHT to its maturity.
Be advised, however, that these codes are intended for research use only. The HHT method is still under
the protection of various Patents (listed below) held by NASA. Those interested in commercial applications
of HHT should contact NASA through the following methods:
NASA Goddard Technology Transfer Office at (301) 286-5804.
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