改良式本質模態分解法在訊號處理之應用

Reformed Intrinsic Mode Decomposition and its Application for Signal Processing

陳思予(Szu-Yu Chen)

指導教授 ： 吳順德

國立臺灣師範大學/科技學院/機電科技研究所/碩士(2009年)

摘要

訊號處理在科學以及工程領域上皆是很重要的課題。自然界的訊號，大多都是非穩態(時變)、非線性過程，故往往得到的訊息包含了雜訊的部分。傳統的傅立葉轉換，其處理的訊號限制為：線性、穩態過程，所以並不能處理大部分的訊號特性。經驗模態分解法(Empirical Mode Decomposition, EMD)對於非線性、非穩態訊號提供一種多尺度、適應性的解析方式，這個方法大大改善了上述的限制。本論文針對多位學者提出此演算法三大課題的改進方式：停止準則、包絡線與邊界效應，作歸納與比較。另外，簡單介紹有關EMD基底的正交性條件、分解上的限制以及基底重建問題。針對文獻提到片段式線性訊號的研究，啟發了本論文對改良式本質模態分解法(Reformed Intrinsic Mode Decomposition, RIMD)的靈感，而片段式線性之概念最大的特點是可以得到較快速的分解法。本研究利用此概念求得之中值點建立出包絡線均值，並對真實訊號之應用上提出以下的方法：以立方雲線聯結中值點；以原始訊號的比例大小聯結中值點，找出包絡線均值。改良式本質模態分解法不但能大大降低演算法的計算量，並且減少在邊界效應極值點選取上之考量，這將會使得訊號在篩選程序中之平穩性以及對稱性大幅的提升。最後，以模擬以及測試訊號透過改良式本質模態分解法拆解出之結果，進行試驗結果之分析與討論。

關鍵字

改良式本質模態分解法 ； 經驗模態分解法 ； 片段式線性 ； 非穩態訊號 ； 雜訊濾除

並列摘要

Signal processing is very important for science and engineering researches. Real world signals are often noisy, non-stationary, and obtained from nonlinear systems. However, the majority of signal processing algorithms proposed in the literature such as Fourier transform are better suited for analyzing the linear stationary signals with weak noise. Empirical Mode Decomposition (EMD) provides a powerful tool for adaptive multi-scale analysis of nonlinear and non-stationary signals. In this thesis, the proposed improvement way of three main topics on the algorithm, stopping criterion, envelope and boundary effect, were summarized and compared. In addition, we make a brief introduction involving orthogonality condition of basis functions, the limitation of decomposition capacity and reconstruction issue of basis functions. It inspired us to propose the Reformed Intrinsic Mode Decomposition (RIMD) by the study of piecewise linear signals in the literature. The best feature of piecewise linear processing is to obtain the faster decomposition efficiency. In this study, we utilize this notion to get middle points and then establish the mean envelope, and propose following methods for the application of real signals: connecting middle points by cubic spline, connecting middle points by the propotion of the original signal, and finding the mean envelope. RIMD is not only reducing the computational cost but also decreasing the selection of extrema for the boundary effect. It will make signals smoother and more symmetric in the sifting process. At last, the results of decomposition using RIMD for the simulated and testing signals were analysized and discussed.

並列關鍵字

reformed intrinsic mode decomposition ； empirical mode decomposition ； piecewise linear ； non-stationary signals ； signal de-noising

參考文獻

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