1. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Hilbert-Huang Transform(HHT) Presenter: Yu-Hao Chen ID:R98943021 2010/05/07

2. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P2 Outline  Author  Motivation  Hilbert Transform  Instantaneous frequency(IF)  Flow chart  Theory  Intrinsic Mode Function(IMF)  Empirical Mode Decomposition(EMD)  Time–Frequency analysis  Application  Problem  Summary

3. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P3 Norden E. Huang ( 黃鍔 )  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

4. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P4 Motivation  To deal with nonlinear and non-stationary signal  To get Instantaneous frequency(IF) [5]

5. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P5 Hilbert Transform  The Hilbert transform can be thought of as the convolution of s(t) with the function h(t) = 1/(πt)  Derive the analytic representation of a signal

6. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P6 Instantaneous Frequency(IF)  s(t) = β + cos(t)  (1) β = 0: IF is the constant  (2) 0 < β < 1: IF has been oscillating  (3) β > 1: IF has been negative [3]

7. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P7 Flow Chart [4][1]

8. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P8 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. [5]

9. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P9 Empirical Mode Decomposition(EMD)(1/8) [1]

10. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P10 Empirical Mode Decomposition(EMD)(2/8) [1]

11. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P11 Empirical Mode Decomposition(EMD)(3/8) [1]

12. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P12 Empirical Mode Decomposition(EMD)(4/8) [1]

13. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P13 Empirical Mode Decomposition(EMD)(5/8) [1]

14. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P14 Empirical Mode Decomposition(EMD)(6/8)   SD IMF [4] [1]

15. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P15 Empirical Mode Decomposition(EMD)(7/8) [1] Sifting Process

16. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P16 Empirical Mode Decomposition(EMD)(8/8)  [4]

17. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P17 Example [5]

18. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P18 Time–Frequency Analysis  Fast Fourier Transform (FFT)  Wavelet Transform  Hilbert-Huang Transform (HHT) FFTWaveletHHT Basisa priori Adaptive Nonlinear Non-stationary Feature Extraction

19. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P19 Application  Geoscience  Biomedical applications  Multimodal Pressure Flow (MMPF)  Financial applications  Image processing  Audio processing  Structural health monitoring

20. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P20 Geoscience  Length of day [5] 1 章年 (19 年 )

21. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P21 Biomedical(1/2)  Multimodal Pressure Flow (MMPF) [5]

22. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P22 Biomedical(2/2)  Doppler blood flow signal analysis [14]  Detection and estimation of Doppler shift [15]

23. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P23 Image Processing  Edge detection [10]  Image denoise [11]  Image fusion [12] P. 23 a. EMD b. Sobel c. Canny ab c

24. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P24 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

25. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P25 P1: Stopping Criterion  Standard deviation(SD)  SD ≤ 0.2~0.3  S number criterion  3 ≤ S ≤ 5  Three parameter method(θ 1,θ 2, α)  Mode amplitude ：  Evaluation function ：  σ(t)< θ 1 in (1- α) σ(t)< θ 2 in α  α ≒ 0.05, θ 1 ≒ 0.05, θ 2 ≒ 10θ 1 [1] [2] [3]

26. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P26 P2: End Effect Problem  End effect of Hilbert Transform [1]  End effect of EMD

27. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P27  End effect of Hilbert Transform  Adding characteristics waves  End effect of EMD  Extension with linear spline fittings near the boundaries P2: Solutions for End Effects maximaminima [6]

28. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P28  Ensemble EMD (EEMD)  Post-processing of EEMD P3: Mode Mixing [1]

29. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P29 P3: Ensemble EMD (EEMD)  Noise n 1 -n m are identical independent distributed.  Ensemble EMD indeed enables the signals of similar scale collated together.  The ensemble EMD results might not be IMFs. [8][7] EEMD IMF ……… … …

30. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P30  Post-processing EEMD can get real IMFs. P3: Post-Processing of EEMD … …

31. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P31 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 [13]

32. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P32 P5: Spline  Cubic B-Spline [5]

33. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P33 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

34. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P34 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. 903–995, 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] 國立中央大學 數據分析研究中心 (RCADA) Available: http://rcada.ncu.edu.tw/intro.htmlhttp://rcada.ncu.edu.tw/intro.html

35. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P35 Reference(2/3) [7] Z. WU and N. E. HUANG, “ENSEMBLE EMPIRICAL MODE DECOMPOSITION:A NOISE-ASSISTED DATA ANALYSIS METHOD”, Advances in Adaptive Data Analysis, Vol. 1, No. 1 pp 1–41,2009 [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.

36. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P36 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

37. ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P37 Thank you