對於訊號分析方面，經驗模態分解法是一個很好用的方法，它具有自適應性(Adaptive)，並能夠處理非線性(Nonlinear)與非穩定(Nonstationary)的訊號，且能在時域上直接訊號拆解，但它會有模態混雜(Mode mixing)的問題。為了解決此問題，Wu與Huang利用白雜訊(White noise)發展了總體經驗模態分解法(Ensemble empirical mode decomposition, EEMD)，但此方法最後的結果是透過多次迭代而產生的，因此運算時間會增加很多。
本文針對語音訊號，我們使用Shaped noise取代白雜訊來加速EEMD收斂的速度，以此降低EEMD迭代的次數。Shaped noise或稱為訊號頻譜相依雜訊(Signal-spectrumdependent noise, SSDN)，它可以隨著輸入訊號的頻譜特性而隨機改變，且具有自適應性的特性，相較於對訊號加入白雜訊，它可以節省對無能量的頻率的運算，大大的省掉多餘的運算，並且降低運算的時間。
本文的實驗中，我們也發現，針對語音訊號，我們可以利用特性較接近語音訊號的雜訊來取白雜訊時，例如粉紅雜訊(Pink noise)與紅雜訊(Brown noise)，也能降低EEMD迭代的次數，降低運算的時間。

In Signal Processing, Empirical mode decomposition (EMD) is one of the useful approaches for processing nonlinear and nonstationary signals. It is adaptive to input signal and could decompose signal straightly in time domain. However, its shortcomings include mode mixing and end effects that usually appear in the decomposed bands. Although a noise-assisted data analysis (NADA) called ensemble empirical mode decomposition (EEMD) has been proposed to circumvent this problem, doing so also results in an inevitably long computation for alleviating the mode mixing. In this paper, we use shaped noise instead of white noise as a disturbance for a fast convergence of EEMD. The signal-spectrum-dependent noise (SSDN) is able to effectively randomize the targeted signal in time domain, and then significantly save the superfluous calculation around the corresponding energy-free frequencies. The experimental results also show that both pink noise and brown noise outperform the white noise in terms of computation for the EEMD of speech-like signal.

[1] H. Press and J. W. Tukey, "Power spectral methods of analysis and their application to problems in airplane dynamics," AGARD Flight Test Manual, vol. 4, pp. 1-41, Jun. 1956.
[2] H. Fuenzalida and B. Rosenbluth, "Prewhitening of climatological time-series," Journal of Climate, vol. 3, no. 3, pp. 382-393, Mar. 1990.
[3] M. J. Link and K. M. Buckley, "Prewhitening for intelligibility gain in hearing aid arrays," Journal of Acoustic Society of America, vol. 93, no. 4, pp. 2139–2145, Apr. 1993.
[4] C. A. Zala, J. M. Ozard, and M. J. Wilmut, "Prewhitening for improved detection by matched-field processing in ice-ridging correlated noise," Journal of Acoustic Society of America, vol. 98, no. 5, pp. 2726–2734, 1995.
[5] R. N. Strickland and H. I. Hahn, "Wavelet transform methods for object detection and recovery," IEEE Transactions on Image Processing, vol. 6, no. 5, pp. 724–735, May 1997.
[6] A. Trucco, "Experimental results on the detection of embedded objects by a prewhitening filter," IEEE Journal of Oceanic Engineering, vol. 26, no. 4, pp. 783–794, 2001.
[7] A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing, John Wiley, UK, 2002.
[8] L. De Lathauwer, B. De Moor, and J. Vandewalle, "A prewhitening-induced bound on the identification error in independent component analysis," IEEE Transactions on Circuits System I:Regular Papers, vol. 52, no. 3, pp. 546–554, 2005.
[9] L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, "Stochastic resonance," Rev. Mod. Phys., vol. 70, no. 1, pp. 223–288, 1998.
[10] N. E. Huang, C. C. Chern, K. Huang, L. Salvino, S. R. Long, and K. L. Fan, "A new spectral representation of earthquake data: Hilbert spectral analysis of station TCU129, Chi-Chi, Taiwan, 21 September 1999," Bulletin of the Seismological Society of America, vol. 91, no. 5, pp. 1310–1338, Oct. 2001.
[11] R. J. Gledhill, Methods for Investigating Conformational Change in Biomolecular Simulations, University of Southampton, UK, 2003.
[12] P. Flandrin, P. Goncalves, and G. Rilling, "EMD equivalent filter banks, from interpretation to applications," Hilbert–Huang Transform: Introduction and Applications, pp. 57–74, Sep. 2005.
[13] N. E. Huang, Z. Shen, and S. R. Long, "A new view of nonlinear water waves : The Hilbert spectrum," Annual Review of Fluid Mechanics, vol. 31, pp. 417–457, Jan. 1999.
[14] Z. Wu and N. E. Huang, "Ensemble empirical mode decomposition: A noise assisted data analysis method," Center for Ocean-Land-Atmosphere Studies, Technical Report series, vol. 193, no. 173, pp. 1-49, Aug. 2005.
[15] 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. 1-49, 2009.
[16] 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," Processing of Royal Society of London Series A-Mathematical Physical and Engineering Sciences, vol. 454, no. 1971, pp. 903-995, Mar. 1998.
[17] G. Rilling, P. Flandrin, and P. Goncalves, "On empirical mode decomposition and its algorithm," IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, pp. 8-11, 2003.
[18] Z. Wu, N. E. Huang, and X. Chen, "The multi-dimensional ensemble empirical mode decomposition method," Advances in Adaptive Data Analysis, vol. 1, no. 3, pp. 339-372, 2009.

[19] N. E. Huang and S. P. Shen, Hilbert-Huang Transform and Its Applications, World Scientific, New Jersey, 2005.
[20] N. E. Huang and N. O. Attoh-Okine, The Hilbert-Huang Transform in Engineering, Taylor & Francis, Boca Raton, 2005.
[21] G. Rilling and P. Flandrin, "One or two frequencies? The empirical mode decomposition answers," IEEE Transactions on Signal Processing, vol. 56, no. 1, pp. 85-95, Jan. 2008.
[22] M. Feldman, "Analytical basics of the EMD: Two harmonics decomposition," Mechanical Systems and Signal Processing, vol. 23, no. 7, pp. 2059-2071, 2009.
[23] J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, "Image analysis by bidimensional emiricla mode decomposition," Image and Vision Computing, vol. 21, no. 12, pp. 1019-1026, Nov. 2003.
[24] Z. Liu and S. Peng, "Boundary processing of bidimensional EMD using texture synthesis," IEEE Signal Processing Letters, vol. 12, no. 1, pp. 33-36, Jan. 2005.
[25] C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensionial EMD," IEEE Signal Processing Letters, vol. 12, no. 10, pp. 701-704, Oct. 2005.
[26] N. J. Kasdin, "Discrete simulation of colored noise and stochastic processes and 1/fα power law noise generation,", Proceedings of the IEEE, vol. 83, no. 5, pp. 802-827, 1995.