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研究生: 黃友亮
Huang, Yu-Liang
論文名稱: 應用疊代式高/低通濾波器於複合波數據修補之研究
Development of an Iterative Filter to Repair a Composite Wave with Missing Data
指導教授: 鄭育能
Jeng, Yih-Nen
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2005
畢業學年度: 93
語文別: 中文
論文頁數: 78
中文關鍵詞: 疊代式濾波器小波轉換數據修補複合波拆解
外文關鍵詞: iterative filter, wave decomposition, data repairing, Morlet transform
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  •   本文應用移動式高斯平滑法做為疊代式濾波器,對潮汐之波形所組合成的複合波數據進行拆解和修補。對於單一和少數連續數據之空缺點,疊代式濾波器可以自動修補之。然而對於兩頻率相近的波所組合而成的複合波,本文所應用的波拆解法尚不能成功的將此複合波拆解出兩個獨立的波,因此本文發展出針對各波形修補的簡易方法。
      
      對於較長時間的空缺數據點,若複合波波長大於空缺時間的根號2倍,空缺數據可以疊代式濾波器自動修補之。若波長小於空缺時間波形的根號2倍,將使用簡易的修補方法,對各個短波長的波形進行修補。本文以屏東後壁湖漁港和台東成功漁港的水位數據為例,說明複合波的拆解和數據修補的過程。本文並以強化型小波轉換法將經過修補的複合波,轉換成為時頻圖,以檢驗各個標準波之頻率與公認頻率之差異,結果證明本文的修補法能精確的保住各波形之特性,同時也證明強化型小波轉換法具有精準的拆解複合波的能力。

     The iterative filter using the Gaussian smoothing method is employed to decompose and repair a tide data string composed of many tidal wave components. Since the iterative filter can ignore the effect of missing data to certain extent, the tidal wave components can be successively decomposed. However, because the employed wave decomposition method cannot decompose a composite wave found by two wave components whose frequencies close to each other, three beats are found. For those wave components whose wavelengths are larger than the square root of two times the drop-out period, the missing data can be satisfactorily achieved by merely applying the filter. For a longer period of missing data, an iterative technique is developed to repair the data. The tide data of the Houbihu harbor in Pingtung at south part of Taiwan during the period of Jan. 1 through Dec. 31/2001 and the Cheng-Kung harbor in Taitung at east part of Taiwan during the period of Aug.1/2002 through Jul.31/2004 are employed to demonstrate the procedure of wave decomposition and data repairing. Finally, the enhanced Morlet transform is employed to examine the repaired composite waves. Results show that the frequencies of all the standard tide waves are precisely captured and even exhibit the frequency variations in some standard tides not understood before. It means that the present data repairing technique is helpful. Moreover, it is proven that the enhanced Morlet is a new powerful tool for time-frequency analysis.

    中文摘要.......................................I 英文摘要......................................II 誌謝.........................................III 目錄..........................................IV 表目錄........................................VI 圖目錄.......................................VII 符號說明....................................XIII 第一章 緒論...................................1 1.1研究動機與目的..............................1 1.2文獻回顧....................................2 第二章 理論分析...............................4 2.1移動式最小平方誤差法........................4 2.2疊代式高斯平滑法與複合波的拆解..............5  2.2.1疊代式高斯平滑法[2-5]...................5  2.2.2複合波的拆解............................7 2.3數據修補....................................8 2.4強化的Morlet小波轉換法.....................15 第三章 結果與討論............................18 3.1簡易修補法的測試...........................18  3.1.1數據空缺為兩天的修補測試...............19  3.1.2數據空缺為九天的修補測試...............20  3.1.3以小波轉換法分析複合波數據.............21 3.2屏東後壁湖漁港.............................23 3.3台東成功漁港...............................31 第四章 結論與未來工作........................37 參考文獻......................................38 自述..........................................77 著作權聲明....................................78

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