Graduate Institute of Electronics Engineering NTU HilbertHuang TransformHHT
Graduate Institute of Electronics Engineering, NTU Hilbert-Huang Transform(HHT) Presenter: Yu-Hao Chen ID: R 98943021 2010/05/07 ACCESS IC LAB
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Outline v Author v Motivation v Hilbert Transform v Instantaneous frequency(IF) v Flow chart v Theory v Intrinsic Mode Function(IMF) v Empirical Mode Decomposition(EMD) v Time–Frequency analysis v Application v Problem v Summary P 2
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Norden E. Huang (黃鍔) v Career and Experience v Research Scientist, NASA (1975 -2006) v National Academy of Engineering (2000) v Academia Sinica (2006) v NASA Goddard Space Flight Center (2000 -2006) v Research Center for Adaptive Data Analysis (2006) v Research topic v Engineering Sciences v Applied Mathematical Sciences v Applied Physical Sciences P 3
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Motivation v To deal with nonlinear and non-stationary signal v To get Instantaneous frequency(IF) [5] P 4
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Hilbert Transform v The Hilbert transform can be thought of as the convolution of s(t) with the function h(t) = 1/(πt) v Derive the analytic representation of a signal P 5
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Instantaneous Frequency(IF) v s(t) = β + cos(t) v (1) β = 0: IF is the constant v (2) 0 < β < 1: IF has been oscillating v (3) β > 1: IF has been negative [3] [3] P 6
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Flow Chart [1] [4] P](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-7.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Flow Chart [1] [4] P")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Flow Chart [1] [4] P 7
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Intrinsic Mode Function(IMF) v The number of extrema and zero-crossings must either be equal or differ at most by one. v The mean value of the upper envelope and the lower envelope is zero. [5] P 8
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(1/8) [1] P](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-9.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(1/8) [1] P")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(1/8) [1] P 9
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(2/8) [1] P](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-10.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(2/8) [1] P")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(2/8) [1] P 10
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(3/8) [1] P](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-11.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(3/8) [1] P")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(3/8) [1] P 11
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(4/8) [1] P](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-12.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(4/8) [1] P")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(4/8) [1] P 12
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(5/8) [1] P](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-13.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(5/8) [1] P")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(5/8) [1] P 13
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(6/8) v v SD < 0. 1 => IMF [4] [1] P 14
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(7/8) [1] Sifting](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-15.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(7/8) [1] Sifting")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(7/8) [1] Sifting Process P 15
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(8/8) v [4]](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-16.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(8/8) v [4]")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Empirical Mode Decomposition(EMD)(8/8) v [4] P 16
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Example [5] P 17](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-17.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Example [5] P 17")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Example [5] P 17
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Time–Frequency Analysis v Fast Fourier Transform (FFT) v Wavelet Transform v Hilbert-Huang Transform (HHT) Basis FFT Wavelet HHT a priori Adaptive Nonlinear Non-stationary Feature Extraction P 18
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Application v Geoscience v Biomedical applications v Multimodal Pressure Flow (MMPF) v Financial applications v Image processing v Audio processing v Structural health monitoring P 19
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Geoscience v Length of day 1章年(19年) [5] P 20
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Biomedical(1/2) v Multimodal Pressure Flow (MMPF) [5] P 21
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Biomedical(2/2) v Doppler blood flow signal analysis [14] v Detection and estimation of Doppler shift [15] P 22
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Image Processing v Edge detection [10] v Image denoise [11] v Image fusion [12] a a. EMD b. Sobel c. Canny b c P. 23 P 23
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Problems of HHT v P 1: Stopping criterion v P 2: End effect problem v Hilbert Transform v EMD v P 3: Mode mixing problem v Ensemble EMD (EEMD) v Post-processing of EEMD v P 4: Speed of computing v P 5: Spline P 24
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 1: Stopping Criterion v Standard deviation(SD) [1] v SD ≤ 0. 2~0. 3 v S number criterion v 3 ≤ S ≤ 5 v Three parameter method(θ 1, θ 2, α) [2] [3] v Mode amplitude： v Evaluation function： v σ(t)< θ 1 in (1 - α) σ(t)< θ 2 in α v α ≒ 0. 05, θ 1 ≒ 0. 05, θ 2 ≒ 10θ 1 P 25
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 2: End Effect Problem v End effect of Hilbert Transform [1] v End effect of EMD P 26
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 2: Solutions for End Effects v End effect of Hilbert Transform v Adding characteristics waves v End effect of EMD v Extension with linear spline fittings near the boundaries maxima minima [6] P 27
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 3: Mode Mixing v Ensemble EMD (EEMD) v Post-processing of EEMD [1] P 28
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 3: Ensemble EMD (EEMD) v Noise n 1 -nm are identical independent distributed. v Ensemble EMD indeed enables the signals of similar scale collated together. v The ensemble EMD results might not be IMFs. [7] [8] EEMD IMF … … … P 29
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 3: Post-Processing of EEMD v Post-processing EEMD can get real IMFs. … … P 30
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 4: Speed of Computing v The processing time of HHT is dependent on complexity of the data and criterions of the algorithm v HHT data processing system(HHT-DPS) v Implementation of HHT based on DSP [13] P 31
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU P 5: Spline v Cubic B-Spline [5] P 32
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Conclusion v The definition of an IMF guarantees a well-behaved Hilbert transform of the IMF v IMF represents intrinsic signature of physics behind the data v Although there are still many problems in HHT, HHT has lots of applications in all aspects P 33
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(1/3) [1] N. E. Huang,](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-34.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(1/3) [1] N. E. Huang,")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU 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. html P 34
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(2/3) [7] Z. WU and](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-35.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(2/3) [7] Z. WU and")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU 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, pp. 841 -845. P 35
![ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(3/3) v [13] H. Li](http://slidetodoc.com/presentation_image_h/d01315ae8dd648bc9c0abb68d8bfb0d5/image-36.jpg "ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(3/3) v [13] H. Li")
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Reference(3/3) v [13] H. Li and Z. Li, etc. , ” Implementation of Hilbert-Huang Transform (HHT) Based on DSP”, International Conference on Signal Processing, vol. 1, 2004 v [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 P 36
ACCESS IC LAB Graduate Institute of Electronics Engineering, NTU Thank you P 37
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