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.