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How it Works
Limitations of Previous Methods
Many applications that involve signal or data processing require the use of transforms such as the Fast Fourier Transform (FFT) or Discrete Fourier Transform (DFT). These transforms allow a signal or data set that satisfies certain conditions to be converted to the frequency domain. Once in the frequency domain, the signal or data set can be analyzed, encoded, or modulated for transmission. The transform can then be used again to return the signal to the time domain once decoded or demodulated.
The methods described above can be applied to linear and stationary signals and data. However, they cannot be applied to nonlinear or nonstationary signals or data sets. A Wavelet Transform can be used on nonlinear signals with gradual inter-wave frequency modulation but cannot be used with signals that have intra-wave modulation (i.e., a group of signals that vary over time). When used with nonlinear and nonstationary signals, current transform methods and technologies may result in reduced quality or accuracy.
Given that many applications in communications, sonar, seismic analysis, acoustics, optics, and medicine require the analysis of multiple signals that are nonlinear and/or nonstationary, new transform technologies are needed.
How HHT Resolves Limitations with Previous Methods
NASA's Goddard Space Flight Center has resolved this limitation with the Hilbert-Huang Transform technology. HHT allows for the accurate transform of nonlinear and/or nonstationary signals, while maintaining the highest level of accuracy. In addition, this technology also provides the same results as the Fourier Transform when applied to linear signals; thus, HHT offers a complete solution to all signal processing needs.
HHT is applied to a signal in the same manner as other transforms, such as the Fourier Transform or Wavelet Transform, and it can be used either in software or hardware form. For software, HHT can be incorporated as a plug-in for use with mathematical or analytical programs or as a stand-alone program. For hardware, HHT can be programmed into a field-programmable gate array (FPGA) or fabricated as an application-specific integrated circuit (ASIC).
The HHT algorithms accurately analyze physical signals via the following steps:
- Instantaneous frequencies are calculated based on the Empirical Mode Decomposition method when intrinsic mode functions (IMFs) are generated for complex data.
- A Hilbert transform converts the local energy and instantaneous frequency derived from the IMFs to a full energy-frequency-time distribution of the data (i.e., a Hilbert spectrum).
- The physical signal is filtered by reconstruction from selected IMFs.
- A curve can be fitted to the filtered signal. (Curve fitting might not have been possible with the original, unfiltered signal.)
Winner of the Federal Laboratory Consortium (FLC) award for excellence in technology transfer, this technology is a highly efficient, adaptive, and user-friendly general computational method. Compared to current transform methods and technologies, HHT offers improved accuracy and yields results with more physical meaning than existing analysis tools that tend to obscure or discard valuable information.
Testing
The HHT algorithms have been implemented in software and tested. Some testing has been conducted for medical applications, specifically the following:
- Blood pressure data from pulmonary artery of a rat
- Pulmonary blood pressure signals in response to step changes in oxygen concentration in breathing gas
- Heart pulse interval comparing sleep apnea condition to nonapnea condition
- Epileptic seizure heart pulse data
Figures summarizing the results of that testing can be found in U.S. Patent 6,381,559. Additional data and results are proprietary and confidential.
The Hilbert Huang Transform Data Processing System (HHT-DPS) was developed at GSFC as a software implementation of the HHT algorithms. It has undergone some testing and has exhibited superior results.
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NASA has filed seven patents and one copyright related to the HHT technology.
Issued patents:
- Application of HHT to Financial Data Analysis for Define Volatility and Trend (GSC-14807-1)
- Stability Spectrum Through Hilbert-Huang Transform (GSC-14833-1)
- 6,990,436: Computing Frequency by Using Generalized Zero-crossing Applied to Intrinsic Mode Functions (issued 1/06; GSC-14608-1 )
- 6,901,353: Computing Instantaneous Frequency by Normalizing Hilbert Transform (issued 5/05; GSC-14673-1)
- 6,862,558: Empirical Mode Decomposition for Analyzing Acoustical Signals (issued 3/05; GSC-13817-4)
- 6,738,734: Empirical Mode Decomposition Apparatus, Method and Article of Manufacture for Analyzing Biological Signals and Performing Curve Fitting (issued 5/04; GSC-13817-5)
- 6,631,325: Computer Implemented Empirical Mode Decomposition Method Apparatus, and Article of Manufacture Utilizing Curvature Extrema (issued 10/03; GSC-13817-2)
- 6,381,559 Empirical Mode Decomposition Apparatus, Method, and Article of Manufacture for Analyzing Biological Signals and Performing Curve Fitting (issued 4/02; GSC-13817-3)
- 6,311,130 Computer Implemented Empirical Mode Decomposition Method, Apparatus, and Article of Manufacture Using Curvature (issued 10/01; GSC-13909-1)
- 5,983,162 Computer Implemented Empirical Mode Decomposition Method, Apparatus, and Article of Manufacture (issued 9/99; GSC-13817-1)
Copyrights:
- Hilbert-Huang Transform Data Processing System (GSC-14591-1)
- Computer Implemented Empirical Mode Decomposition Method, Apparatus, and Article of Manufacture (GSC-13909-1)
Related patents:
The following patents are not part of the HHT licensing package offered herein since they have been developed by people and/or organizations outside of the NASA Goddard HHT innovator team. Potential partners/licensees should perform their own due diligence to determine their interest in the technologies listed below.
- 6,507,798 Time-frequency Dependent Damping via Hilbert Damping Spectrum (The United States Navy)
Point of Contact: Henry Strunk; 301-227-1529; strunkh@nswccd.navy.mil
- 6,192,758 Structure Safety Inspection (Kang Huang)
Point of Contact: Kang Huang; (214) 651-8757
- 09/729,138 Three Dimensional Empirical Mode Decomposition Analysis Apparatus and Method (filed 11/00; GSC-14302) (not yet published)
- 60/435,790 Multi-Point Vibrometer for Measurement of Surface Vibrations (NASA Langley Research Center)
Point of Contact: Gary Fleming; 757-864-6664; gary.a.fleming@nasa.gov
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HHT Technical Information
- NASA Bridges Safety Gap, FLC NewsLink, January 2007
Nancy Pekar, NASA Goddard
(Visit the FLC NewsLink Web Site)
- HHT Tutorial, Presentation, July 21, 2004
Norden E. Huang
- Overview of HHT Processing and the HHT-DPS
White paper on the software code implementing HHT
Norden E. Huang
- A confidence limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis, Proceedings of the Royal Society of London, A (2003) v. 459, 2317-2345
Abstract: By using various adjustable parameters in the sifting processes of the EMD method, an ensemble of Intrinsic Mode Function (IMF) sets is generated. Based on such an ensemble, we introduce a statistical measure in a form of confidence limits for the Intrinsic Mode Functions, and subsequently, the Hilbert spectra. The confidence limit on EMD HSA is applied to the daily data of Length-of-Day between 1962 and 2000. Interesting features such as the influence of the El Niño events on the length of day and the Metonic cycle are clearly revealed. Furthermore, the confidence limit also reveals the uncertainty of the weak El Niño events for the middle 60s and earlier 90s. This addition makes the EMD HSA methods more rigorous and useful.
Norden E. Huang, M.C. Wu, S.R. Long, S.S. Shen, W. Qu, and P. Gloerson
- The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis, Proceedings of the Royal Society of London, A (1998) v. 454, 903-995
Although this paper describes HHT in great depth, it does not contain all of the needed methodology to implement HHT.
Norden E. Huang, Z. Shen, and S. R. Long, M. C. Wu, E. H. Shih, Q. Zheng, C. C. Tung, and H. H. Liu
- Hilbert-Huang Transform Data Processing System (HHT-DPS)
Hilbert-Huang Transform Advanced Technology Briefing
Semion Kizhner, Thomas P. Flatley, Norden E. Huang, Karin Blank, and Darrell Smith
NASA Goddard Space Flight Center, March 24, 2003
- On the Hilbert-Huang Transform Data Processing System Development, IEEE, (Submitted April, 2003) [Link to be added when available.]
Norden E. Huang
- HHT Basics and Applications
For Speech, Machine Health Monitoring, and Bio-Medical Data Analysis
Norden E. Huang
March 24, 2003
HHT Applications
 Overview
- Hilbert-Huang Transform and Its Applications, World Scientific, Singapore
Ed by Norden E. Huang and Samuel S. P. Shen
- The Hilbert-Huang Transform in Engineering, Taylor Francis, Boca Raton
Ed by Norden E. Huang and Nii O. Attoh-Okine
- HHT Basics and Applications
For Speech, Machine Health Monitoring, and Bio-Medical Data Analysis by Norden E. Huang
Biomedical Applications
- Beyond the Fourier Transform: Coping with Nonlineary, Nonstationary Time Series, presented at Harvard's Heart Rate Variability 2006: Techniques, Applications, and Future Directions conference by Norden E. Huang, May 2006.
- Application of the Hilbert-Huang Transform to the Analysis of Molecular Dynamics Simulations, Journal of Physical Chemistry A, American Chemical Society, 10.1021/jp0261758 CCC, published on Web 05/23/2003
S. C. Phillips, R. J. Gledhill, and J. W. Esse
Department of Chemistry, University of Southampton, U.K.
C. M. Edge
GlaxoSmithKline, U.K.
- Travelling Waves in Dengue Hemorrhagic Fever Incidence in Thailand, Nature. [Link to be added when available.]
D. Cummings, R. Irizarry, N. Huang, T. Endy, A. Nisakak, K. Ungchusak, and D. Burke
- Hilbert-Huang Transform: A method for analyzing nonlinear and nonstationary data
NASA Medical Technology Summit
Norden E. Huang
Pasadena, CA, February 12, 2003
- Empirical Mode Decomposition: A useful technique for neuroscience?
Review of Huang et al, Procedures of the Royal Society of London, A (1998) v. 454, 903-995 -
Robert Liu
Computational Journal Club, January 11, 2002
- Nonlinear Indicial Response of Complex Nonstationary Oscillations as Pulmonary Hypertension Responding to Step Hypoxia, Procedures of the National Academy of Sciences, USA, 96, 1834-1839, 1999.
W. Huang, Z. Shen, Norden E. Huang, Y.C. and Fung
- Engineering Analysis of Biological Variables: An Example of Blood Pressure over One Day, Procedures of the National Acadademy of Sciences, USA, 95, pp.4816-4821, April, 1998.
W. Huang, Z. Shen, Norden E. Huang, and Y.C. Fung
- Engineering Analysis of Intrinsic Mode and Indicial Response in Biology: the Transient Response of Pulmonary Blood Pressure to Step Hypoxia and Step Recovery, Procedures of the National Academy of Science, USA, 95, pp 12766-12771, 1998
W. Huang, Z. Shen, Norden E. Huang, and Y. C. Fung
- Potential HHT Applications in Biomedical Signal Analysis
C-K Peng, Ph.D., Beth Israel Deaconess Medical Center Harvard Medical School, NIH Research Resource for Complex Physiologic Signals
Environmental Applications
- Comparison of Interannual Intrinsic Modes in Hemispheric Sea Ice Covers and Other Geophysical Parameters, IEEE Transactions on Geoscience and Remote Sensing, 41, 1-14, 2003 (Submitted April 7, 2003)[Link to be added when available.]
P. Gloerson and Norden E. Huang
- An Anatomy of Drift Waves in Equatorial Spread F Event, Geophysical Research Letters, 28, 3107-3110, 2001
K.Y. Chen, H. C. Yeh, S. Y. Su, C. H. Liu, and Norden E. Huang
- Application of EMD-HHT Method to Identify Near-Fault Ground Motion Characteristics and Structural Responses, Bulletin of the Seismological Society of America, 2001, 91, 1,339-1,357, 2001
Chin-Hsiung Loh, Tsu-Chiu Wu, and Norden E. Huang
- Spectral Anysis of the Chi-Chi Earthquake Data: Station TUC129, Taiwan, September 21, Bulletin of the Seismological Society of America, 91, 1,310-1,338, 2001.
Norden E. Huang, C. C. Chern, K. Huang, L. Salvino, S. R. Long, and K. L. Fan
- The Ages of Large-Amplitude Coastal Seiches on the Caribbean Coast of Puerto Rico, Journal Physical Oceanography, 30, 2001-2012, 2000
Norden E. Huang, H. H. Shih, Z. Shen, S. R. Long, and K. L. Fan
- A New View of Nonlinear Water Waves – The Hilbert Spectrum, Annual Review of Fluid Mechanics, 31, 417-457, 1999.
Norden E. Huang, Z. Shen, and R. S. Long
- In Search of an Elusive Antarctic Circumpolar Wave in Sea Ice Extents, 1978-1996. Polar Research, 18 (2), 167-173, 1999.
P. Gloersen, and Norden E. Huang
- Interannual Variability in the South China Sea from Expendable Bathythermograph Data, Journal of Geophysical Research, 104, 23, 509-23, 523, 1999.
Liping Wang, C. Koblinsky, S. Howden, and Norden E. Huang
- The Development of the South Asian Summer Monsoon and the Intraseasonal Oscillation, Journal of Climate, 12, 2054:2075, 1999
M-L Wu, S. Schubert and Norden E. Huang
- Spectral Description and Simulation of Non-stationary Random Processes by Hilbert Transform
Abstract that discusses HHT
Y. K. Wen and Ping Gu, University of Illinois at Urbana-Champaign
- Wave and Group Transformation By A Hilbert Spectrum
WorldSciNet paper wrote: "The Hilbert-Huang Transform (HHT) method for nonlinear and nonstationary time series analysis is applied to wave field data from the nearshore area. The frequency-time distribution of the energy, designated as a Hilbert spectrum is utilized for the examination of the sea waves and their group structure. The key feature of the HHT method is Empirical Mode Decomposition (EMD), which provides a unique basis for expansion of the data, derived from and based on the data. The necessary condition for the existence of wave grouping is determined based on the results of Empirical Mode Decomposition of the data. An attempt is made to investigate the transformation of the sea waves by examination of the decomposition components along the beach profile. The cross-shore variations of the group characteristics are studied. The Hilbert-Huang Transform method provides new insights on the wave and group cross-shore transformation."
Financial Applications
- Applications of Hilbert-Huang Transform to Nonstationary Financial Time Series Analysis, Journal Applied Stochastic Models in Business and Industry. [Link to be added when available.]
N.E. Huang, S. R. Long, W. D. Qu, S. S. Shen, J. Zhang
Industrial/Structural Applications
- A Multi-point Vibrometer using the HHT for Signal Analysis
HHT Advanced Analysis Software Technology Briefing
Gary A. Fleming, NASA Langley Research Center, Hampton, VA; Keith D. Grinstead, Jr., Swales Aerospace, Inc.; John S. Tripp, NASA Langley Research Center
NASA Goddard Space Flight Center, March 24, 2003
- A new method for nonlinear and nonstationary time series analysis Stochastic Structural Dynamics, Ed. B. F. Spencer, E. A. Johnson, Balkema, Rotterdam, 559-564., 1999
Norden E. Huang, Z. Shen, S. R. Long, and M. J. Huang
- Application of the Hilbert-Huang Transform in Machine Tool Fault Detection
Gary G. Leisk, Tufts University, Mechanical Engineering
Other Applications
- Data Analysis with the Empirical Mode Decomposition Method and the Hilbert Spectra
Benny Cheng, Jet Propulsion Laboratory, Pasadena, CA
HHT Awards & Honors
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- Service to America Medal
Dr. Norden E. Huang's Hilbert-Huang Transform won one of the prestigious Service to America Medals in the Science and Environment category for 2006 from the Partnership for Public Service.
- NASA Exceptional Space Act Award
In 1999, 2002, 2003 and 2004, the NASA Headquarters Inventions and Contributions Board recognized the Hilbert-Huang Transform with Space Act awards and cited it "as one of the most important discoveries in the field of applied mathematics in NASA history."
- NASA Government Invention of the Year
The invention of the year ceremony was held at NASA Headquarters on Thursday, June 5th. This event recognized Dr. Norden E. Huang's mathematical method called Computer Implemented Empirical Mode Decomposition Method, also known as the Hilbert-Huang Transformation (HHT) Method.
- R&D100 Awards Recognize Hilbert Huang Transform
Aerospace Technology Innovation; Volume 9, Number 6; November/December 2001; Advanced Technologies
"HHT is groundbreaking because it produces more precise, meaningful and interpretable results of nonlinear and nonstationary data."
- Norden Huang Wins 2001 FLC Award for Excellence in Technology Transfer
"Norden Huang, Senior Fellow and Chief Scientist for Oceanography, has won the Federal Laboratory Consortium (FLC) Award for Excellence in Technology Transfer for his work on the Hilbert-Huang Transform (HHT)."
- NASA Exceptional Space Act Award
In 1999, 2002, and 2003, the NASA Headquarters Inventions and Contributions Board recognized the Hilbert-Huang Transform with Space Act awards and cited it "as one of the most important discoveries in the field of applied mathematics in NASA history."
- NASA Wallops Researchers Received Technology Leadership Award
Two researchers from the Wallops Flight Facility (Wallops Island, Va.) were part of two NASA Goddard Space Flight Center (Greenbelt, Md.) projects that were selected for the 1999 Government Technology Leadership Award sponsored by the Government Executive Magazine.
Dr. Steven R. Long and William Krabill were part the Hilbert-Huang Transform team and the Airborne Light Detection and Ranging (LIDAR) Topographic Mapping System team, respectively.
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