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

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

ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P3 Norden E. Huang ( 黃鍔 )  Career and Experience  Research Scientist, NASA ( )  National Academy of Engineering (2000)  Academia Sinica (2006)  NASA Goddard Space Flight Center ( )  Research Center for Adaptive Data Analysis (2006)  Research topic  Engineering Sciences  Applied Mathematical Sciences  Applied Physical Sciences

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]

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

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]

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

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]

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

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

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

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

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

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

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

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

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

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

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

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

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

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]

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

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

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]

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

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]

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

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 ……… … …

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

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]

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

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

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 [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 [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 [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 [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 [6] 國立中央大學 數據分析研究中心 (RCADA) Available:

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 [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 [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 [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

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 , July 2007

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