本文應用移動式最小平方誤差法發展出一套全新的疊代型濾波器。本文證明移動式最小平方誤差法是一種擴散型數值法，若用之為濾波器，則在頻譜圖上之切斷頻率附近會產生一個寬的過渡區。新的疊代型濾波器可以有效地縮減過渡區的頻寬。假設數據串的頻譜圖上有一沒有任何波的空窗區，則可以應用新的疊代式高斯平滑法或移動式最小平方誤差法，經使用小心的選擇高斯核因子 和疊代次數，成功地拆解出相同的長短波形。此一結果與濾波器的階次無關。因此，可以用一個簡單低階疊代的方法去獲得高階的濾波結果。若使用新的疊代法去處理含有斷點的數據串，將會產生數值上的蘭矩(RUNGE)振盪現象。振盪波從斷點位置起向兩邊衰減，第一個振盪波的波長只與高斯函數之平滑參數 成正比率，但振幅則只與斷點的高低大小有關。斜率及高次導函數的不連續性所產生的振盪誤差不大，且其振幅和波長都和平滑參數 成比率，因此若使用合理小的 ，可以不需特意處理導函數的斷點誤差。本文並提出一種簡易數據串之分段濾波法，對各段分別做平滑，數值證明此種簡易法可以消除振盪性誤差。

　　The discrete moving least squares methods weighted by the Gaussian function are shown to be diffusive. These methods have wide transition zones in the vicinity of the cut-off frequency selected to filter a given data string. An iterative scheme has been proposed to effectively reduce the width of the transition zone and a sufficient condition to achieve the convergence is derived. If the frequency of a given data string is distinguishable, by careful selections of the Gaussian kernel factor, , and iterative number, , one can successfully separate the wave formations of the high and low frequency parts. This separation of the two frequency parts is unique and is independent of the order of the least squares methods. Consequently, one can employ a simpler low-order iterative scheme to achieve high-order solutions. The method has been successfully applied to several designed examples. A simple two-dimensional example is also tested to demonstrate the validity of the method in complex multi-dimensional situations. If the filtered data string involves a discontinuous jump, the iterative filter will give a smooth data with the Runge numerical oscillation phenomenon. The oscillatory wavelength is approximately proportional to the smoothing factor while the amplitude is approximately proportional to the jump magnitude. The induced oscillations across a jump of low and high order derivatives of a data string are not significantly large as comparing with that of the data string. In order to eliminate the oscillation, a strategy of piecewise smoothing is proposed where the boundaries of each segment is determined by some criteria.

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