本文旨在發展近似的一維複合波拆解法。本文首先提出修正極值點的預測法和強化cubic spline內插法，以改進黃鄂等人所發展的經驗式模態分解法。數值測試顯示本文所提的修正法，雖仍無法改進原方法應用數值法處理，沒有理論依據，而出現許多的缺點，但補捉不同頻率的波的功能確實有明顯的改善。

本文試著發展另外一套新的波之分解法，我們以希爾伯特(Hilbert)轉換式為工具，透過數學衍算將希爾伯特(Hilbert)轉換式發展為高低頻濾波器，其中數據資料可為無限或有限區域，但當資料來源為有限區間時，必須加上高斯核函數使濾波的過程局部化，以降低數值計算上的誤差，而由數值測試顯示當複合波的各模態的頻率有足夠大的頻差時，本文所發展的波分解法，在波的振幅頻率都為常數，且有明顯的頻率差時，可以分解出高低頻波，並且能進一步得到複合波各模態的相關資料，如頻率、振幅、相位角等。但當頻率為可變時，只有在有明顯的頻率差時才能順利的拆解各個波。但本文確實為合理的一維波之拆解法，提出一個可行的發展方向。

The main concerning of this study is to develop an approximate one-dimensional wave decomposition method. Huang’s Empirical Mode decomposition Method is first improved by two modifications: the Gaussian smoothing with adaptive kernel is employed to estimate the maximum and minimum points of the wave; and the cubic spline interpolation method is replaced by a robust interpolation. The new interpolation employs the cubic spline interpolation whenever a modified monotonic condition is satisfied. However, if the condition is violated the monotonic M3A cubic interpolation of Hyuanh is employed. Numerical tests show that the capability of decomposing single waves are signifi- cantly improved.

In this study, a new wave decomposition method is also proposed. The Hilbert Transform is modified by adding a sine function so that it can be a basic tool of the new high and low pass filters. For finite range of data, a Gaussian kernel is embedded to localize the data so that the finite boundary error can be effectively reduced. Numerical experiments show that the localization technique is effective whenever simple extrapolation is done on two ends. For a wave composing with constant amplitudes and frequencies waves (and they are clearly separated), the proposed method can effectively decompose all the waves. However, for slowing varying frequencies (with apparent frequency differences), the proposed method can also provide a good decomposition. Although the method is failed for a more general case, it does point out a new direction of developing an one-dimensional approximate wave decomposition.

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