本文改進鄭所發展之應用修正型之Hilbert 轉換式的高低通濾波器。首先將高低通濾波器所得的結果，應用三次曲線移動式最小平方誤差法平滑之，以改進高頻誤差。若複合波的頻率有明顯的差距時，數值測試顯示這種改進可以得到令人滿意的結果。應用三次曲線移動式最小平方誤差法的原因，是其曲率解析能力遠高於快速的高斯平滑法。但高頻誤差移除法在複合波的頻率差距並不很明顯時，無法有效的提供合理的單一波。本文並初步探討線性化最小平方誤差法之波拆解法，將振幅和cosine 函數相乘所造成的高度非線性，用線性化法配何三次曲線分段內插法近似之。此種近似造成的函數之自由度不匹配，會使最終結果產生高頻誤差，用三次曲線移動式最小平方誤差法平滑後，再依次使用振幅修正之最小平方誤差法及相角修正之最小平方誤差法，以改進精確度，最後仍舊用三次曲線移動式最小平方誤差法平滑之。本文初步使用均勻節點於三次曲線分段內插法，數值測試的精確度令人滿意，顯示此種方法據有進一步發展的潛力。

This thesis employs the cubic moving least squares method to smear the high frequency error of the result of the Jeng high/low passed filter via the modified Hilbert transforms. When the frequency difference is large enough, numerical tests show that this improvement can provide a satisfactory wave decomposition. The reason of employing the cubic
moving least squares method is that it has a better curvature resolution capability than the fast Gaussian smoothing method.On the other hand, if the frequency difference is not significantly large, the smearing is not effective.
This paper also studies a procedure of linearized wave decomposition via the least squares method. The high non-linearity introduced by the production between the amplitude and cosine function is linearized and is
equipped with the cubic spline interpolation. Since the degrees of freedom of the linearized product between the amplitude and cosine function can not be properly settled, the penalty of the high frequency error is always presented. After employing the cubic moving least squares
method to smear the high frequency error, two least squares method basing on the amplitude modification and phase modification are applied, respectively.
Finally, the cubic moving least squares method is again employed to provide the decoupled wave. Because of the first study, a uniform nodal spacing strategy is employed. A numerical test gives a satisfactory result which reflects the potential of the proposed wave decomposition procedure.

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