請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65392完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 葉丙成 | |
| dc.contributor.author | Che-Shuo Chang | en |
| dc.contributor.author | 張哲碩 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:40:18Z | - |
| dc.date.available | 2017-07-27 | |
| dc.date.copyright | 2012-07-27 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-25 | |
| dc.identifier.citation | [1] S.G. Mallat, A wavelet tour of signal processing: the sparse way, Elsevier /Academic Press, 2009.
[2] Norden E. Huang, Zheng Shen, StevenR. Long, Manli C. Wu, Hsing H. Shih, Quanan Zheng, Nai-Chyuan Yen, Chi Chao Tunga, and Henry H. Liu, “The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings Royal Society of London, pp. 903–995, 1998. [3] Norden E. Huang and Samuel S P Shen, Hilbert-Huang Transform and Its Applications, World Scientific, 2005. [4] Imre M. Janosi and Rolf M uller, “Empirical mode decomposition and correlation properties of long daily ozone records,” Phys. Rev. E, vol. 71, pp. 056126, May 2005. [5] K.T Coughlin and K.K Tung, “11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method,” Advances in Space Research, vol. 34, no. 2, pp. 323–329, 2004. [6] C. Sweeney-Reed and S. Nasuto, “A novel approach to the detection of synchronisation in eeg based on empirical mode decomposition,” Journal of Computational Neuroscience, vol. 23, pp. 79–111, 2007. [7] Patrick Flandrin, Gabriel Rilling, and Paulo Goncalves, “Empirical mode decomposition as a filter bank,” IEEE SIGNAL PROCESSING LETTERS, vol. 11, pp.112–114, 2004. [8] G. Rilling and P. Flandrin, “One or two frequencies? the empirical mode decomposition answers,” Signal Processing, IEEE Transactions on, vol. 56, no. 1, pp. 85–95, jan. 2008. [9] Yanyang Zia Keyu Qia, Zhengjia Heb, “Cosine window-based boundary processing method for emd and its application in rubbing fault diagnosis,” Mechanical Systems and Signal Processing, vol. 21, pp. 1750–2760, 2007. [10] Kan Zeng and Ming-Xia He, “A simple boundary process technique for empirical mode decomposition,” vol. 6, pp. 4258 –4261 vol.6, sept. 2004. [11] Gabriel Rilling, Patrick Flandrin, and Paulo Goncalves, “On empirical mode decomposition and its algorithms,” IEEEEURASIP workshop on nonlinear signal and image processing, vol. 3, pp. 8–11, 2003. [12] R. Deering and J.F. Kaiser, “The use of a masking signal to improve empirical mode decomposition,” vol. 4, pp. iv/485 – iv/488 Vol. 4, march 2005. [13] O. Niang, E. Delechelle, and J. Lemoine, “A spectral approach for sifting process in empirical mode decomposition,” Signal Processing, IEEE Transactions on, vol. 58, no. 11, pp. 5612 –5623, nov. 2010. [14] Y. Kopsinis and S. McLaughlin, “Investigation and performance enhancement of the empirical mode decomposition method based on a heuristic search optimization approach,” Signal Processing, IEEE Transactions on, vol. 56, no. 1, pp. 1 –13, jan. 2008. [15] ZhaoHua Wu and Norden E. Huang, “Ensemble empirical mode decomposition: A noise-assisted data analysis method,” Advances in Adaptive Data Analysis, vol. 1, no. 1, pp. 1–41, march 2009. [16] R.A. Johnson and D.W. Wichern, Applied multivariate statistical analysis, Pearson Prentice Hall, 2007. [17] L.E. Spence, A.J. Insel, and S.H. Friedberg, Elementary Linear Algebra: A Matrix Approach, Prentice Hall, 2007. [18] G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996. [19] S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Advanced Mathematics. Dover Publications, 1993. [20] Bengt Fornberg, “Generation of finite difference formulas on arbitratily spaced grids,” Mathematics of Computation, vol. 51, no. 184, pp. 699–706, Oct. 1988. [21] M. Unser, “Splines: a perfect fit for signal and image processing,” Signal Processing Magazine, IEEE, vol. 16, no. 6, pp. 22 –38, nov 1999. [22] A.N. Akansu and R.A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets, Telecommunications Series. Academic Press, 2001. [23] S.S. Haykin, Adaptive filter theory, Prentice-Hall information and system sciences series. Prentice Hall, 2002. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65392 | - |
| dc.description.abstract | 經驗模態分解是一個被廣泛應用在各種領域的訊號分解方法。此演算法是基於利用仿樣內差來內插局部極值點，而這個步驟確造成我們在分析演算法性能與數學性質時的困難。至今為止，我們對於經驗模態分解的認識大多來自於實際觀察的結果。此外，經驗模態分解在使用上也缺乏彈性，無法滿足不同的需求。在這一個研究中，我們提出的基於濾波器的經驗模態分解提供了參數化的演算法，可以做不同的調整。透過此方法我們可以調整內在模態函數其終止頻率的下降速度。並且，演算法所對應的濾波器組和其分解訊號結果都可以預先知道並受控制。因此我們可以把基於濾波器的經驗模態分解應用在濾波器組上。此演算法的另外一個特色是他能夠抵抗雜訊與間歇訊號。他除了能夠避免邊界處理和模態混合的問題外，還是個有效率的方法。在數值結果中顯示此演算法在實際訊號與自回歸移動平均訊號普遍有比較好的表現，頻譜重疊的情況也有減少。這些討論與結果或許有助於我們對經驗模態分解相關的演算法發展其理論框架。 | zh_TW |
| dc.description.abstract | The empirical mode decomposition (EMD) has been widely applied to many research fields for decomposing the signal. The algorithm is based on the spline interpolation of local extreme points. This procedure makes it difficult to analyze the performance and the corresponding mathematical properties. Thus till now most of knowledges about EMD are based on practical observations. In addition, the EMD itself has little flexibility to adapt to different requirement. In this work, the proposed filter-based empirical mode decomposition (FB-EMD) provides a parametrized algorithm adjustable for different settings. In this way it is possible to change the decreasing rate of the cutoff frequency of the intrinsic mode function (IMF). Moreover, the equivalent filter bank and the decomposition results are predictable and controllable. This enables us to apply the FB-EMD to the filter bank design. Another feature of the FB-EMD is that the algorithm is resistant to the noise and intermittencies. While being free from the boundary process and the mode mixing problem, the proposed method is also efficient. The numerical results show that in general the FB-EMD have better performance in real signals and autoregressive moving-average signals. The spectral overlap is also reduced. These discussions and the numerical results is helpful for developing a theoretic framework for the EMD based algorithm. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:40:18Z (GMT). No. of bitstreams: 1 ntu-101-R99942038-1.pdf: 8777396 bytes, checksum: 81baf93f9b4105a17b036b524c452460 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Background Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Vector decomposition . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 Sifting process . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Filter bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Signal Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.1 Empirical Mode Decomposition . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Partial Differential Equation Based Empirical Mode Decomposition . . . 14 3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4 Filter-based Empirical Mode Decomposition . . . . . . . . . . . . . . . . . . . 21 4.1 The Family of the Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Interpolation Point Selection . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3 Adaptive Spline-filter Interpolation . . . . . . . . . . . . . . . . . . . . . 25 4.4 Decomposition Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.5.1 Decomposition results with different B-spline . . . . . . . . . . . 31 4.5.2 Decomposition results of different filter length and order . . . . . 32 4.5.3 Double loop FB-EMD using curvature extrema as interpolation points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5 Analysis of the FB-EMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1 Analysis and Evaluation of the Equivalent Filter of FB-EMD . . . . . . . 44 5.1.1 Decreasing rate of the oscillatory frequency . . . . . . . . . . . . 44 5.1.2 Evaluation of the decreasing rate beta from data . . . . . . . . . . . 48 5.1.3 Evaluation of the cutoff frequency . . . . . . . . . . . . . . . . . 49 5.2 Filter Bank Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3.1 Analytic results of beta0 . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3.2 Decreasing rate beta . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3.3 Convergence Behavior . . . . . . . . . . . . . . . . . . . . . . . 56 6 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.2 Spectral Overlap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.3.1 Performance of FB-EMD . . . . . . . . . . . . . . . . . . . . . . 64 6.3.2 Performance evaluation for the autoregressive signal . . . . . . . 66 7 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 | |
| dc.language.iso | en | |
| dc.subject | 趨勢訊號 | zh_TW |
| dc.subject | 經驗模態分解 | zh_TW |
| dc.subject | 內插 | zh_TW |
| dc.subject | 非穩態訊號 | zh_TW |
| dc.subject | empirical mode decomposition | en |
| dc.subject | trend signal | en |
| dc.subject | interpolation | en |
| dc.subject | non-stationary signal | en |
| dc.title | 以濾波器為基礎的經驗模態分解與其在濾波器組上的應用 | zh_TW |
| dc.title | Filter-based Empirical Mode Decomposition and Its Application to Filter Bank Design | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 呂良鴻,丁建均,蘇柏青 | |
| dc.subject.keyword | 經驗模態分解,趨勢訊號,內插,非穩態訊號, | zh_TW |
| dc.subject.keyword | empirical mode decomposition,trend signal,interpolation,non-stationary signal, | en |
| dc.relation.page | 75 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-07-25 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
| 顯示於系所單位： | 電信工程學研究所 | |
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