本研究提出了一個以有理式為模型發展的過濾數據數值方法，用來降低在離散連續動態輸出裡的雜訊訊號。但是對於系統，只要加入濾除器就可能會產生不良的影響。本研究提出的雜訊濾除器是能有效的降低殘餘雜訊(Residual Noise)的大小並且可以忽略經由濾波後所產生的誘發誤差(Induced Error)，藉由平滑數據序列來達到降低數據的雜訊。因此本論文先用電腦模擬一組實驗數據，利用所設計之濾除器去濾除雜訊，探討哪種參數調整的濾除器對於系統會有較佳之性能以及能將雜訊降減到多少，最後在幫助使用者歸納參數公式。

This paper proposes a numerical technique to design data filter. The proposed filter is developed for the reduction of additive and data noise contained in the discrete output of implicit continuous dynamics that is modeled by a ration function. However, adding controller will emerge bad effect for any system. So, the merits of this technique include an orders of magnitude reduction in the residual noise level and a negligible induced error on the filtered signal. Reduction in data noise is achieved by smoothing the data sequence. First, we simulate a set of data by computer and filtrate data noise by proposed filter. We investigate which parameter has best performance and which level of noise can be reduced. At last ,we offer envelope function for user.

[1] J .T.H. Chan (1996) it Optimal output feedback regulator - A numerical synthesis approach for input-output data, ASME/JDSMC V01.118, 1996.
[2] J.T.H. Chan, An LQ controller with a prescribed pole region, A data-based design approach, ASME/JDSMC, vol.119, No.2, pp.271-277, 1997..
[3] Lennart Ljung and Torsten Sodertrom. Theory and practice of recursive identification. The MIT Press, Cambridge, Ma., 1983.
[4] Savitzky, A., and M.J.E. Golay (1964), Smoothing and differentiation of data by simplified least squares procedures, Analytical Chemistry, 36, 1627-1639.
[5] Steinier, Jean; Termonia, Yves; Deltour, Jules (1972). Smoothing and difierentiation of data by simplified least square procedure. Analytical Chemistry 44 (11): 1906V9.
[6] Marchand, P., and L. Marmet (1982), Binomial smoothing filter: A way to avoid some pitfalls of least square polynomial smoothing? Rev. Sci. Instrum., 54, 1034-41.
[7] O’Haver, T., (2008) Intro_to Signal ProcessingSmoothing, http://terpconnect.umd.edu/ toh / spectrum / Smoothinghtml.html
[8] E.. Jacobsen and R. Lyons (2003), The Sliding DFT, Signal Processing Magazine vol.20, issue 2, pp. 74V80.
[9] E. Jont B. Allen (1977). Short Time Spectral Analysis, Synthesis, and Modification by Discrete Fourier Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing. ASSP-25 (3): 235V238, June.
[10] J. Chen, P. Jonsson, M. Tamura, Z. Cu, B. Matsushita, and L. Eklundh (2004). A simple method for reconstructing a high-quality ndui time-series data set based on the sauitzky-golay filter. Remote Sensing of Environment, 91(3-4):332 V 344.
[11] Raymond G. Jacquot, Modern digital control systems, Marcel Dekker,Inc., New York, N.Y.. pp.37-40, (1981).