# 使用迭代式高斯法與傾斜極值篩選法解決經驗模態分解法中的混波現象

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2011

## Abstract

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.