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

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。

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.