1998年黃鍔等人提出了一種可以用來處理非線性、非穩態訊號的時頻分析工具，經驗模態分解法(Empirical mode decomposition, EMD)。經驗模態分解法可以將訊號拆解成數個零均值、近似單成分的本質模態函數(Intrinsic Mode Function, IMF)。可以比傅立葉分析(Fourier analysis)多處理非線性及非穩態訊號的優點，使得經驗模態分解法已被應用在各個不同的領域。然而經驗模態分解法存在著一些缺點例如停止準則、邊界效應、混波現象(mode mixing)…等。本論文提出了一個結合迭代式高斯法(iterative Gaussian filter)與傾斜極值篩選法(oblique-extrema based sifting process, OEMD)流程，可以用來解決經驗模態分解法中的主要缺點:混波問題。不論迭代式高斯法或傾斜極值篩選法都不是解決混波現象的完美解答，其中一個方法太耗時而另一個只能處理混波現象的特定種類。由實驗結果可以發現，本論文的流程的確可以有效阻止混波現象的發生。

An ideal algorithm for nonlinear and non-stationary data analysis was proposed by Huang et al. in 1998, as known as Empirical Mode Decomposition (EMD). Comparing to Fourier analysis assuming the time series data is linear and stationary, EMD is a method capable of analyzing not only linear and stationary but also nonlinear and non-stationary. With this useful feature, EMD has been applied to many fields. However, lacking theoretical foundation, there are some drawbacks in EMD, such as sifting stop criterion, boundary effect, mode mixing, etc. To fix the mode mixing problem, the main drawback of EMD, a process is presented in this paper, which combines iterative Gaussian diffusive filter (IGDF) with oblique-extrema based sifting process (OEMD) since either IGDF or OEMD is not the perfect solution for mode mixing problem, for the reasons that one of them is only able to solve specific problems and the other one is too time-consuming. The experiments presented in this paper indicating that the proposed process works as expected.

[1] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.C. Yen, C. C. Tung and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings: Mathematical, Physical and Engineering Sciences , vol. 454, no.1971, pp.903-995, 1998.
[2] R. T. Rato, M. D. Ortigueira and A.G. Batista, “On the HHT, its problems, and some solutions,” Mechanical Systems and Signal Processing, vol. 22, pp. 1374-1394, 2008.
[3] N. E. Huang, M. L. 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 spectral analysis,” Proceedings of The Royal Society A-Mathematical Physical and Engineering Sciences, vol. 459, pp. 2317-2346, 2003.
[4] C. Junsheng, Y. Dejie and Y. Yu, “Research on the intrinsic mode function (IMF) criterion in EMD method,” Mechanical Systems and Signal Processing, vol. 20, pp. 817-824, 2006
[5] B. Xuan, Q. Xie and S. Peng, “EMD sifting based on bandwidth,” IEEE Signal Processing Letters, vol. 14, no. 8, 2007
[6] K. Zeng and M. X. He, “A simple boundary process technique for empirical mode decomposition,” Proceedings of the IEEE International Geoscience and Remote Sensing Symposium Proceedings (IGARSS ’04), vol. 6, pp. 4258-4261, Anchorage, Alaska, USA, 2004
[7] M. G. Frei and I. Osorio, “Intrinsic time-scale decomposition: Time-frequency-energy analysis and real-time filtering of non-stationary signals,” Proceedings of The Royal Society A-Mathematical Physical and Engineering Sciences, vol. 463, pp. 321, 2007
[8] Z. Zhidong and W. Yang, “A new method for processing end effect in empirical mode decomposition,” in Proceedings of 2007 IEEE Conference on Communications, Circuits and Systems, pp. 841-845, 2007
[9] Z. Qingjie, Z. Huayong and S. Lincheng, “A new method for mitigation of end effect in empirical mode decomposition,” IEEE 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics, pp.400-403, 2010
[10] 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
[11] M. Feldman, “Analytical basics of the EMD: Two harmonics decomposition,” Mechanical Systems and Signal Processing, vol.23, no.7, pp.2059-2071, 2009
[12] G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answer,” IEEE Transactions on Signal Processing, vol. 56, no. 1, pp. 85-95, 2008
[13] Q. Chen, N. Huang, S. Riemenschneider and Y. Xu, “A B-spline approach for empirical mode decompositions,” Advances in Computational Mathematics, vol. 24, no. 1-4, pp. 171-195, 2006
[14] S. R. Qin and Y. M. Zhong, “A new envelope algorithm of Hilbert-Huang transform,” Mechanical Systems and Signal Processing, vol. 20, pp. 1941-1952, 2006
[15] G. G. S. Pegram, M. C. Peel and T. A. McMahon, “Empirical mode decomposition using rational splines: an application to rainfall time series,” Proceedings of The Royal Society A-Mathematical Physical and Engineering Sciences, vol. 464, pp. 1483-1501, 2008
[16] Y. Kopsinis and S. McLaughlin, “Improved EMD using doubly-iterative sifting and high order spline interpolation,” EURSIP Journal on Advances in Signal Processing, vol. 2008, no. 120, 2008
[17] Z. Xu, B. Huang and K. Li, “An alternative envelope approach for empirical mode decomposition,” Digital Signal Processing, vol. 20, no. 1, pp. 77-84, 2010
[18] A. Roy and J. F. Doherty, “Improved signal analysis performance at low sampling rates using raised cosine empirical mode decomposition,” IEEE Electronics Letters, vol. 46, no. 2, pp. 176-177, 2010
[19] H. Hong, X. Wang and Z. Tao, “Local integral mean-based sifting for empirical mode decomposition,” IEEE Signal Processing Letters, vol. 16, no. 10, 2009
[20] El Hadji S Diop, R. Alexandre and A. O. Boudraa, “Analysis of intrinsic mode functions a PDE approach,” IEEE Signal Processing Letters, vol. 17, no. 4, 2010
[21] P. Frank Pai, “Online tracking of instantaneous frequency and amplitude of dynamical system response,” Mechanical Systems and Signal Processing, vol. 24, pp. 1007–1024, 2010
[22] 林家齊，「改善經驗模態分解法混波問題與計算效率之研究」，國立台灣師範大學，碩士論文，民國99年6月
[23] M. D. Wheeler and K. Ikeuchi, “Iterative smoothed residuals a low-pass filter for smoothing with controlled shrinkage,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, no. 3 pp. 334-337, 1996
[24] Y. N. Jeng, P. G. Huang and Y. C. Cheng, “Decomposition of one-dimensional waveform using iterative Gaussian diffusive filtering methods,” Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, vol.464, no. 2095, pp. 1673-1695, 2008
[25] 維基百科，低通濾波器，http://zh.wikipedia.org/zh-tw，2011年7月24日更新(中文)
[26] Z. J. Yang, L. G. Yang and C. M. Qing, “An oblique-extrema-based approach for empirical mode decomposition,” Digital Signal Processing, vol.20, no. 3 pp. 699-741, 2010
[27] G. L. Xu, X. T. Wang and X. G. Xu, “Time varying frequency-shifting signal assisted empirical mode decomposition method for AM FM signals,” Mechanical Systems and Signal Processing, vol.23, no. 8, pp.2458-2469, 2009
[28] R. Deering and J. F. Kaiser, “The use of a masking signal to improve empirical mode decomposition,” Processing IEEE ICASSP, Philadelphia, USA, vol. 4, pp. 485-488, 2005