1 of 9 2/28/2009 6:42 PM

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1 1 of 9 2/28/2009 6:42 PM Analyze nonlinear, nonstationary signals with Hilbert-Huang Transform NASA Goddard Space Flight Center (GSFC) has developed a new signal processing technology called the Hilbert-Huang Transform (HHT). GSFC seeks to license its HHT technology to private industry for use in commercial applications. The HHT technology is a highly efficient, adaptive, and user-friendly set of algorithms capable of analyzing time-varying processes. Designed specifically for nonlinear and nonstationary signals, HHT can be used to analyze data in a wide variety of applications. The algorithms also provide increased accuracy when used to analyze linear and stationary signals. When linear, stationary datasets are used, HHT provides the same solution as the Fast Fourier Transform. However, Fourier Transforms are unsuitable for applications that use nonlinear and/or nonstationary signals. In addition, other technologies, such as wavelet transforms, cannot resolve intra-wave frequency modulation, which occurs in signal systems composed of multiple varying signals. HHT can be used in these applications to provide an accurate method for analyzing nonlinear and/or nonstationary signals or data. NASA has filed 7 patents on this method (3 granted and 4 pending). Dr. Norden Huang's HHT method was recognized as the NASA Government Invention of the Year on June 5, This method was also the winner of the Government Technology Leadership Award in 2000; the Federal Laboratory Consortium Technology Leadership award in 2000; and the R&D 100 award in The Hilbert-Huang Transform has earned Dr. Huang the NASA Exceptional Space Act award with the citation, "[Dr. Huang's new method] is one of the most important discoveries in the field of applied mathematics in NASA history." For this pioneer work on nonlinear, nonstationary data analysis, Dr. Huang was elected to the National Academy of Engineering in Additional technical details are presented below. For more information about this licensing opportunity, please contact: Caroline Stetter-Neel, (304) Precision: More precise time-frequency representation of signal data and sharper filter performance than with "Fourier-based" methods Flexibility: Designed for processing nonlinear and nonstationary signals, but flexible enough to analyze any data (linear or nonlinear) and stationary or nonstationary signals Accuracy: Preserves intrinsic properties of data; offers a microscopic view of data not limited by the uncertainty principle; and does not impose a priori assumptions on data, as in Fourier methods (i.e., that assume linear and stationary data) Easy Implementation: Easy and inexpensive to implement in software or hardware Real-time operation: Operates and yields physically meaningful results in real time Multifunctionality: Generates IMFs through an adaptive algorithm from a data set with which other methods fail; examines previously unattainable results for aiding diagnosis of abnormal conditions; and provides new, quantitative measurements that enhance understanding of underlying phenomena

2 2 of 9 2/28/2009 6:42 PM Medical Sensors Devices/instruments Imaging Design (e.g., tissue engineering, drug discovery) Acoustics, noise, and vibration Highway noise Submarine design Machine vibration analysis Speech/sound analysis Speaker/sound recognition Environmental Industrial Fluids Surface temperature data Radiometer data Connecting environmental changes to phenomena Sonar, radar, lidar Seismology Machine monitoring and failure prediction Electrical circuits Heat conduction and convection Nondestructive testing Structures Numerical simulation of fluid flow Nondestructive testing Shock loading Business/Finance Economic data Market data How it Works Testing 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

3 3 of 9 2/28/2009 6:42 PM 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: 1. Instantaneous frequencies are calculated based on the Empirical Mode Decomposition method when intrinsic mode functions (IMFs) are generated for complex data. 2. 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). 3. The physical signal is filtered by reconstruction from selected IMFs. 4. 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. Issued Copyright Pending in Progress Related NASA has filed seven patents and one copyright related to the HHT technology. Issued patents: 6,381,559 Empirical Mode Decomposition Apparatus, Method, and Article of Manufacture for Analyzing Biological Signals and Performing Curve Fitting (issued 4/02; GSC ) 6,311,130 Computer Implemented Empirical Mode Decomposition Method, Apparatus, and Article of Manufacture Using Curvature (issued 10/01; GSC ) 5,983,162 Computer Implemented Empirical Mode Decomposition Method, Apparatus, and Article of Manufacture (issued 9/99; GSC ) Copyrights: Hilbert-Huang Transform Data Processing System (GSC ) Computer Implemented Empirical Mode Decomposition Method, Apparatus, and Article of

4 4 of 9 2/28/2009 6:42 PM Manufacture (GSC ) Pending patents: Normalized Amplitude Hilbert Transform (NAHT): A New Algorithm for Computing Instantaneous Frequency (filed 7/03; GSC ) 10/073,957 Empirical Mode Decomposition for Analyzing Acoustical Signals (filed 2/02; GSC ) 09/282,424 Implemented Empirical Mode Decomposition Method, Apparatus, and Article of Manufacture for Analyzing Biological Signals and Performing Curve Fitting (filed 12/01; GSC ) (not yet published) 09/082,523 Extrema Continuation in Part Allowed (filed 5/98; GSC ) (not yet published) in progress: Time Frequency Analysis Based on Extrema Sifting (GSC ) Related patents: 6,507,798 Time-frequency Dependent Damping via Hilbert Damping Spectrum (The United States Navy) Point of Contact: Henry Strunk; ; strunkh@nswccd.navy.mil 6,192,758 Structure Safety Inspection (Kang Huang) Point of Contact: Kang Huang; (214) /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; ; gary.a.fleming@nasa.gov HHT Technical Information HHT HHT Awards & Honors HHT Technical Information Overview of HHT Processing and the HHT-DPS White paper on the software code implementing HHT Norden E. Huang The Royal Society (2002 in press): A confidence limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis [Link to be added when available.] 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 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. 3. Hilbert E. Huang, M.C. Wu, S.R. Long, S.S. Shen, W. Qu, and P. Gloerson The Royal Society (1998): The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis, Procedures of the Royal Society of London, A454, , 1998 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 4. Hilbert-Huang Transform Data Processing System (HHT-DPS) Hilbert-Huang Transform Advanced Technology Briefing

5 5 of 9 2/28/2009 6:42 PM 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 For Speech, Machine Health Monitoring, and Bio-Medical Data Analysis Norden E. Huang March 24, 2003 HHT Overview 1. Hilbert-Huang Transform and Its, World Scientific, Singapore Ed by Norden E. Huang and Samuel S. P. Shen 2. The Hilbert-Huang Transform in Engineering, Taylor Francis, Boca Raton Ed by Norden E. Huang and Nii O. Attoh-Okine 3. HHT Basics and For Speech, Machine Health Monitoring, and Bio-Medical Data Analysis by Norden E. Huang Biomedical 1. Beyond the Fourier Transform: Coping with Nonlineary, Nonstationary Time Series, presented at Harvard's Heart Rate Variability 2006: Techniques,, and Future Directions conference by Norden E. Huang, May Application of the Hilbert-Huang Transform to the Analysis of Molecular Dynamics Simulations, Journal of Physical Chemistry A, American Chemical Society, /jp CCC, published on Web 05/23/ 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, 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, , 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 , April, 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 , 1998 W. Huang, Z. Shen, Norden E. Huang, and Y. C. Fung 10. Potential HHT in Biomedical Signal Analysis C-K Peng, Ph.D., Beth Israel Deaconess Medical Center Harvard Medical School, NIH Research Resource for Complex Physiologic Signals

6 6 of 9 2/28/2009 6:42 PM Environmental 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, , 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, 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, , 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, , Norden E. Huang, Z. Shen, and R. S. Long In Search of an Elusive Antarctic Circumpolar Wave in Sea Ice Extents, Polar Research, 18 (2), , P. Gloersen, and Norden E. Huang Interannual Variability in the South China Sea from Expendable Bathythermograph Data, Journal of Geophysical Research, 104, 23, , 523, 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 11. 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 1. 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 1. 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

7 7 of 9 2/28/2009 6:42 PM 2. NASA Goddard Space Flight Center, March 24, 2003 A new method for nonlinear and nonstationary time series analysis Stochastic Structural Analysis, Ed. B. F. Spencer, E. A. Johnson, Balkema, Rotterdam, , 1999 Norden E. Huang, Z. Shen, S. R. Long, and M. J. Huang 3. Application of the Hilbert-Huang Transform in Machine Tool Fault Detection Gary G. Leisk, Tufts University, Mechanical Engineering Other 1. Data Analysis with the Empirical Mode Decomposition Method and the Hilbert Spectra Benny Cheng, Jet Propulsion Laboratory, Pasadena, CA HHT Awards & Honors 1. 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. 2. 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." 3. 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)." 4. 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." 5. 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. Licensing and Partnering For information and forms related to the technology licensing and partnering process, please visit Goddard's Licensing and Partnering page.

8 8 of 9 2/28/2009 6:42 PM Medical applications brochure Other applications brochure If you would like additional information, contact: Caroline Stetter-Neel, (304) Visit NASA Goddard's Technology Transfer Program Web site: Technology transfer and commercialization are an important part of the mission at NASA's Goddard Space Flight Center. Goddard's technology, expertise, and facilities are a national asset that can be used to develop new products and processes that benefit the United States. These benefits include increasing the Nation's competitiveness, improving the balance of trade, and enriching the lives of the citizenry.

9 9 of 9 2/28/2009 6:42 PM and answers will be posted as they are received. Q: I've seen comments posted on the Internet implying that HHT has a number of shortcomings. Is this accurate? A: Since HHT was published, many researchers and developers have attempted their own implementations of the algorithm, leading to the varying results to which you are referring. These results are typically a result of the programmer s level of understanding and interpretation of the algorithm. The HHT-DPS software that NASA is making available for licensing was developed in conjunction with Dr. Norden Huang, inventor of the HHT algorithm. As such, it provides robust and reliable results that fully and accurately implement the algorithm. Q: What are the hardware and software requirements for the HHT trial? A: The program has been tested on Win2k and WinXP. Memory and other hardware needs depend on your processing requirements. Larger data sets will require more of those resources to run properly. This technology is owned by the National Aeronautics and Space Administration (NASA). More information is available from NASA s Goddard Space Flight Center. [Some documents on this page are Adobe Acrobat PDF format files. Download this free Adobe Acrobat Reader.] [Link opens new browser window.] Fuentek, LLC Phone: (919) , Fuentek, LLC. All Rights Reserved.