Hilbert-Huang Transform(HHT)

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Hilbert-Huang Transform(HHT)

• Presenter Yu-Hao Chen
• IDR98943021
• 2010/05/07

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Outline

• Author
• Motivation
• Hilbert Transform
• Instantaneous frequency(IF)
• Flow chart
• Theory
• Intrinsic Mode Function(IMF)
• Empirical Mode Decomposition(EMD)
• TimeFrequency analysis
• Application
• Problem
• Summary

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Norden E. Huang (??)

• Career and Experience
• Research Scientist, NASA (1975-2006)
• National Academy of Engineering (2000)
• Academia Sinica (2006)
• NASA Goddard Space Flight Center (2000-2006)
• Research Center for Adaptive Data Analysis (2006)
• Research topic
• Engineering Sciences
• Applied Mathematical Sciences
• Applied Physical Sciences

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Motivation

• To deal with nonlinear and non-stationary signal
• To get Instantaneous frequency(IF)

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Hilbert Transform

• The Hilbert transform can be thought of as the
  convolution of s(t) with the function h(t)
  1/(pt)
• Derive the analytic representation of a signal

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Instantaneous Frequency(IF)

• s(t) ß cos(t)
• (1) ß 0 IF is the constant
• (2) 0 lt ß lt 1 IF has been oscillating
• (3) ß gt 1 IF has been negative

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Flow Chart
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1
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Intrinsic Mode Function(IMF)

• The number of extrema and zero-crossings must
  either be equal or differ at most by one.
• The mean value of the upper envelope and the
  lower envelope is zero.

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Empirical Mode Decomposition(EMD)(1/8)
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Empirical Mode Decomposition(EMD)(2/8)
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Empirical Mode Decomposition(EMD)(3/8)
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Empirical Mode Decomposition(EMD)(4/8)
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Empirical Mode Decomposition(EMD)(5/8)
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Empirical Mode Decomposition(EMD)(6/8)

• SD lt 0.1 gt IMF

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1
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Empirical Mode Decomposition(EMD)(7/8)
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Sifting Process
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Empirical Mode Decomposition(EMD)(8/8)

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Example
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TimeFrequency Analysis

• Fast Fourier Transform (FFT)
• Wavelet Transform
• Hilbert-Huang Transform (HHT)

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Application

• Geoscience
• Biomedical applications
• Multimodal Pressure Flow (MMPF)
• Financial applications
• Image processing
• Audio processing
• Structural health monitoring

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Geoscience

• Length of day

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Biomedical(1/2)

• Multimodal Pressure
• Flow (MMPF)

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Biomedical(2/2)

• Doppler blood flow signal analysis 14
• Detection and estimation of Doppler shift 15

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Image Processing

• Edge detection 10
• Image denoise 11
• Image fusion 12

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Problems of HHT

• P1 Stopping criterion
• P2 End effect problem
• Hilbert Transform
• EMD
• P3 Mode mixing problem
• Ensemble EMD (EEMD)
• Post-processing of EEMD
• P4 Speed of computing
• P5 Spline

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P1 Stopping Criterion

• Standard deviation(SD)
• SD 0.20.3
• S number criterion
• 3 S 5
• Three parameter method(?1,?2, a)
• Mode amplitude
• Evaluation function
• s(t)lt ?1 in (1- a)
• s(t)lt ?2 in a
• a ? 0.05, ?1 ?0.05,
• ?2 ? 10?1

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3
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P2 End Effect Problem

• End effect of Hilbert Transform

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• End effect of EMD

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P2 Solutions for End Effects

• End effect of Hilbert Transform
• Adding characteristics waves
• End effect of EMD
• Extension with linear spline fittings near the
  boundaries

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P3 Mode Mixing

• Ensemble EMD (EEMD)
• Post-processing of EEMD

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P3 Ensemble EMD (EEMD)

• Noise n1-nm are identical independent
  distributed.
• Ensemble EMD indeed enables the signals of
• similar scale collated together.
• The ensemble EMD results might not be IMFs.

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P3 Post-Processing of EEMD

• Post-processing EEMD can get real IMFs.

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P4 Speed of Computing

• The processing time of HHT is dependent on
  complexity of the data and criterions of the
  algorithm
• HHT data processing system(HHT-DPS)
• Implementation of HHT based on DSP

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P5 Spline

• Cubic B-Spline

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Conclusion

• The definition of an IMF guarantees a
  well-behaved Hilbert transform of the IMF
• IMF represents intrinsic signature of physics
  behind the data
• Although there are still many problems in HHT,HHT
  has lots of applications in all aspects

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Reference(1/3)

• 1 N. E. Huang, Z. Shen, etc. The empirical
  mode deomposition and the Hilbert spectrum for
  nonlinear and non-stationary time series
  analysis, Proceedings of the Royal Society, vol.
  454, no. 1971, pp. 903995, March 8 1998.
• 2 N. E. Huang, M. C. Wu, S. R. Long, S. S. P.
  Shen, W. Qu, P. Gloersen and K. L. Fan, A
  Confidence Limit for the Empirical Mode
  Decomposition and Hilbert Spectrum Analysis,
  Proc. R. Soc. Lond. A, vol. 459, 2003, pp. 2317-
  2345.
• 3 G. Rilling, P. Flandrin and P. Gonçalvés, On
  Empirical Mode Decomposition and Its Algorithms,
  IEEE-EURASIP Work- shop on Nonlinear Signal and
  Image Processing NSIP-03, Grado, Italy, 8-11 Jun.
  2003.
• 4 J. Cheng, D. Yu and Y. Yang, Research on the
  Intrinsic Mode Function (IMF) Criterion in EMD
  Method, Mechanical Systems and Signal
  Processing, vol. 20, 2006, pp. 817-824.
• 5 Z. Xu, B. Huang and S. Xu, Exact Location of
  Extrema for Empirical Mode Decomposition,
  Electronics Letters, vol. 44, no. 8, 10 Apr.
  2008, pp. 551-552.
• 6 ?????? ???????? (RCADA)
• Available http//rcada.ncu.edu.tw/intro
  .html

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Reference(2/3)

• 7 Z. WU and N. E. HUANG , ENSEMBLE EMPIRICAL
  MODE DECOMPOSITIONA NOISE-ASSISTED DATA ANALYSIS
  METHOD, Advances in Adaptive Data Analysis, Vol.
  1, No. 1 pp 141,2009
• 8 Master thesis Applications of Ensemble
  Empirical Mode Decomposition (EEMD) and
  Auto-Regressive (AR) Model for Diagnosing
  Looseness Faults of Rotating Machinery
• 9 Y. Deng, W. Wang, C. Qian, Z. Wang and D.
  Dai, Boundary-Processing- Technique in EMD
  Method and Hilbert Transform, Chinese Science
  Bulletin, vol. 46, no. 1, Jan. 2001, pp. 954-960.
• 10 J. Zhao and D. Huang, Mirror Extending and
  Circular Spline Function for Empirical Mode
  Decomposition Method, Journal of Zhejiang
  University, Science, vol. 2, no.3, July-Sep.
  2001, pp. 247-252.
• 11 K. Zeng and M. He, A simple Boundary
  Process Technique for Empirical Mode
  Decomposition, IEEE International Geoscience and
  Remote Sensing Symposium IGARSS '04, vol. 6,
  2004, pp. 4258-4261.
• 12 Z. Zhao and Y. Wang, A New Method for
  Processing End Effect in Empirical Mode
  Decomposition, IEEE International Conference on
  Circuits and Systems for Communications ICCSC
  2007, 2007, pp. 841-845.

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Reference(3/3)

• 13 H. Li and Z. Li, etc. , Implementation of
  Hilbert-Huang Transform (HHT)
• Based on DSP, International
  Conference on Signal Processing, vol.1, 2004
• 14 Z. Zhidong and W. Yang ,A New Method for
  Processing End Effect In
• Empirical Mode Decomposition,
  International Conference on
• Communications, Circuits and
  Systems, ICCCAS , pp 841-845, July 2007

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Thank you