改善經驗模態分解法混波問題與計算效率之研究

Abstract

經驗模態分解法(Empirical mode decomposition, EMD)是近年來用於非穩態訊號的時頻分析與濾波工具。此方法能將訊號拆解成數個零均值的單頻段震盪訊號與一個殘餘量，黃鍔稱單頻段訊號為本質模態函數(Intrinsic Mode Function, IMF)。雖然EMD已經在很多領域被證明其有效性，但這個方法仍存在許多的問題亟待被解決，這些問題包含：(1)停止準則之選取;(2)邊界效應;(3)訊號混波現象;(4)篩選程序之效率性。本論文的主要目的是改善混波問題與提升篩選程序的效率。 本論文提出利用微分運算與減少取樣的方式分別改善EMD混波問題與計算效率，實驗結果證實： (1) 透過微分運算提高訊號之振幅比，可以將部份頻段的訊號成分分離出來，使得混波問題大幅降低，並且提高EMD拆解能力。 (2) 透過減少取樣的運算方式減少極值點搜尋與立方雲線內插的計算時間，使得EMD整體的計算效率提升。 本論文的貢獻是改善EMD拆解的計算速度以及提高EMD拆解能力，進而提升訊號分析與濾波的能力。

A new nonlinear technique for time frequency analysis, referred to as empirical mode decomposition (EMD), has recently been pioneered by N.E. Huang et al., for adaptively representing nonstationary signals as sums of zero-mean components, terms Intrinsic Mode Functions (IMFs). Although EMD had been proved its feasibility and efficiency for many applications, some drawbacks and problems are needed to be resolved which including the selection of stop criterion; the process of boundary effect; the mode mixing phenomena; the computational efficiency of sifting process. In this dissertation, the mode-mixing problem and computational efficiency of EMD algorithm is improved by using differential operator and down sampling technique respectively. Several experimental results demonstrate that: 1. The computational cost can be reduced dramatically when the down-sampling technique is applied. 2. The mode-mixing problem can be resolved by applying a differentiail operator to the target signal.