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 本論文首先針對小波函數、小波轉換函數、小波去雜訊合成訊號、遞迴最小平方法、傳統的有益變數法和所提出的小波去雜訊有益變數法，作一概略性的介紹。另外，闡述小波兼具時頻特性的原因。 對於含雜訊的二階開環穩定系統，由閉環路和開環路方式，利用遞迴最小平方法、傳統的有益變數法和小波去雜訊有益變數法，分別辨識出系統參數值並與真實參數作比較。其中，閉環路方式以替續器來產生輸入訊號，開環路方式則以偽隨機二進制序列為輸入訊號。結果顯示：(1)使用小波去雜訊有益變數法優於遞迴最小平方法和傳統的有益變數法; (2)小波去雜訊有益變數法使用於開環路系統又優於閉環路系統。 對於含雜訊的三階開環穩定系統，以偽隨機二進制序列為輸入訊號的開環路方式進行模擬研究，利用遞迴最小平方法、傳統的有益變數法和小波去雜訊有益變數法分別求得系統參數值並與真實參數和賴氏圖作比較。無論由數據比較的結果或由賴氏圖近似的情況來看，小波去雜訊有益變數法皆優於遞迴最小平方法和傳統的有益變數法。 以上結果指出，以偽隨機二進制序列為輸入訊號的開環路方法配合小波去雜訊有益變數法為鑑別含雜訊的開環穩定系統參數最好的方式之一。
 This thesis first discusses the concept of wavelet functions, wavelet transforms, wavelet de-noising, the recursive least-squares method, the conventional instrumental variable method, and the proposed instrumental variable method with wavelet de-noising. In addition, the time-frequency character of wavelet functions is elucidated. A simulation study is conducted on open-loop stable, second-order systems in a closed-loop and an open-loop manner. The system parameters identified by the three methods are compared with their actual values for each system. In the closed-loop operation, the relay is employed to produce the input signal, while in the open-loop operation, the input signal is generated by the pseudo random binary sequence. The simulation results reveal that: (1) The instrumental variable method with wavelet de-noising is superior to the other two methods. (2) The open-loop manner is better than the closed-loop manner. A simulation study is also carried out on third-order systems in open-loop operation where the input signal is generated by the pseudo random binary sequence. The system parameters identified by the three methods are compared by virtue of their actual values and Nyquist plots. The results show that the proposed method is superior to the other two methods. It can be concluded that one of the best methods for parameter identification of open-loop stable systems is the proposed instrumental variable method with wavelet de-noising employed in the open-loop manner.
 中文摘要………………………………………………………………… i 英文摘要……………………………………………………………… iii 表目錄……………………………………………………………………v 圖目錄………………………………………………………………… vii 第一章 緒論………………………………………………. ………..1 1.1 研究動機與目的………………………………………………...1 1.2 文獻回顧………………………………………………………...2 1.3 章節與組織……………………………………………………...5 第二章 小波函數和多層解析度分析……………………………... 6 2.1 多層解析度分析………………………………………….….. 6 2.1.1 多層解析度的近似空間…………………………………..6 2.1.2 多層解析度的細節空間…………………………………..7 2.1.3 多層解析度的特性………………………………………..8 2.2 小波函數………………………………………………….…..10 2.2.1 小波函數和尺度函數…………………………………...10 2.2.2 小波函數的種類………………………………………….11 第三章 小波轉換和去雜訊的合成訊號…………………………......14 3.1 小波轉換……………………………………………………...15 3.1.1 小波轉換之種類和離散小波逆轉換…………………….15 3.1.2 小波轉換在時間頻率定位的能力……………………….16 3.2 去雜訊的合成訊號…………………………………………...20 3.2.1 近似係數和細節係數…………………………………….20 3.2.2 快速離散一維小波分解與合成演算法………………….21 3.2.3 小波去雜訊合成訊號…………………………………….24 第四章 二階離散系統之模擬研究………………………………...26 4.1 含雜訊的二階系統模擬的模式……………………………...26 4.2 線性參數模式鑑別的方法…………………………………...29 4.2.1 遞迴最小平方法求解系統參數………………………….29 4.2.2 傳統有益變數法求解系統參數……………………. ….34 4.2.3 小波去雜訊有益變數法求解系統參數………………….36 4.3 模擬流程……………………………………………………...36 4.3.1 遞迴最小平方法求解系統參數的模擬過程…………….37 4.3.2 傳統有益變數法求解系統參數的模擬過程…………….39 4.3.3 小波去雜訊有益變數法求解系統參數的模擬過程…….41 4.4 結果與討論…………………………………………………...45 4.4.1 二階含雜訊的閉環路系統模擬的結果………………….45 4.4.2 二階含雜訊的開環路系統模擬的結果………………….48 4.4.3 比較二階含雜訊的閉環路與開環路系統模擬的結果….50 第五章 三階離散系統之模擬研究………………………………...88 5.1 含雜訊的三階系統模擬的模式……………………………...88 5.2 模擬步驟……………………………………………………...89 5.3 結果與討論…………………………………………………...92 第六章 結論與未來展望…………………………………………..107 參考文獻………………………………………………………………..109 附錄一 函數的正交………………………………………………..114 附錄二 裡的正交補集合…………………….................115 附錄三 快速一維小波分解與合成理論(簡述) ………………….118 附錄四 模擬程式及Simulink之方塊圖…………………………..123
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 1 小波分解輔助影像紋理區之分塊 2 以小波表達城市幾何表面之新方法 3 小波轉換於分析淺化波浪特性之應用 4 應用類神經網路與小波理論分析地震前地下水位波動 5 利用小波轉換技術於結構振動訊號之解析 6 小波理論應用於週波脫落的偵測與修補及基線解算 7 應用連續柯西小波轉換於結構物之勁度與阻尼矩陣識別 8 建構小波轉換域中預測型濾波器的一種創新方法論及其應用 9 應用小波函數對磁阻尼與磁剛性係數之鑑別 10 語音加強－基於混合式小波臨界值演算法於有色雜訊的刪減 11 以小波係數為基礎之強健性浮水印研究 12 以小波轉換判別紋路影像之研究 13 以小波轉換為基礎的多重解析度邊線追蹤技術 14 多尺度卡曼濾波器組應用於GPS時變通道模式之鑑定

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