• 作者： 陳銘逵; 黃奇; 石延平
• 作者服務機構： 成功大學化工系; 中正大學化學工程研究所; 台灣海洋大學電機系
• 中文摘要： 本文利用Daubechies所提出的小波函數之two-scale關係式，衍導出許多有用的性質。這些性質有助於利用Wavelet-Galerkin法把含有時問多項式係數的微分方程式轉換成代數式，稱為小波迴歸方程式。此外，利用Lagrange插值法，本文也提出一個簡單的轉換公式，可從訊號的抽樣數據轉成小波級數展開式之係數，以此配合所導出的小波迴歸方程式，吾人可將間斷時間系統識別演算法，應用於辨識具時變參數的連續時間系統之參數。因為所導出的小波迴歸方程式不含系統輸出及輸入變數的起始值，故系統參數辨識可批次進行，亦可線上即時執行“
• 英文摘要： The two-scale relation for constructing Daubechies’compactly supported wavelets is exploited toderive some useful properties which allow an ordinary differential equation with time-varying coefficientsto be converted into wavelet regression equations by using the Galerkin method. With the Lagrangeinterpolation technique, a simple transformation formula is derived for obtaining the wavelet-series-expansion coefficients of a continuous-time signal from its sampled data. Through the derived waveletregression equations and the transformation formula, the time-varying parameters of continuous-timesystems can be estimated from their sampled input-output data by using the identification algorithmsdeveloped for discrete-time models.Moreover, the identification process can be performed in a both batchand real-time manner since the converted wavelet regression equations do not involve the initial valuesof the system's input and output variables.
• 中文關鍵字： wavelets; parameter indentification; time-Varying
• 英文關鍵字： --