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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.

http://techtransfer.gsfc.nasa.gov

Or, register your interest at the
following sites:

http://techtransfer.gsfc.nasa.gov/HHT/

http://techtransfer.gsfc.nasa.gov/HHT/HHT-registration.html

HHT related Patents:

1. Computer implemented Empirical Mode Decomposition
apparatus, method and article

of manufacture. US Patent 5,983,162,
Granted Nov. 9, 1999.

2. Computer implemented Empirical Mode Decomposition
apparatus, method and article

of manufacture for two-dimensional
signals. US Patent 6,311,130 B1, Granted Oct. 30,

2001.

3. Empirical Mode Decomposition apparatus, method and
article of manufacture for

analyzing biological signals and
performing curve fitting. US Patent 6,381,559 B1,

Granted Apr. 30,
2002.

4. Computer implemented Empirical Mode Decomposition
apparatus, method and article

of manufacture utilizing curvature extrema. US Patent 6,631,325 B1, Granted Oct 7,

2003.

5. Empirical Mode Decomposition apparatus, method and
article of manufacture for

analyzing biological signals and
performing curve fitting. US Patent 6,738,734 B1,

Granted May 18,
2004.

6. Empirical Mode Decomposition for analyzing
acoustical signals. US Patent 6,862,558

B3, Granted Mar. 1, 2005.

7. Computing instantaneous frequency by normalizing
Hilbert Transform. US Patent

6,901,353 B1, Granted May 31, 2005.

8. Computing frequency by using
generalized zero-crossing applied to Intrinsic Mode

Functions. US Patent 6,990,436 B1,
Granted Jan. 24, 2006.

9.
Ensemble Empirical Mode Decomposition: A Noise Assisted Data
Analysis Method

by
Zhaohua Wu and Norden Huang
Application
Pending 2007.