The Study of Sampling Period and Signal Response in A Specific Digitalized System

特定數位化系統之取樣週期與信號響應研究

陳春明(Chuen-Ming Chen)；鄭永業(Yong-Ya Zheng)

series expansion ； sampled-data system ； model transformation ； 級數展開 ； 取樣系統 ； 模式轉換

台北海洋科技大學學報

11卷2期（2020 / 09 / 01）

183 - 197

英文

In this paper, the interesting problems of a digitalized signal system are studied, it includes the magnitude of sampling period and the different response shape of its sampled-data system. The response can be described as a triangular function, the series expansion concerning the sampling period nΤ will be shown as an important factor. Also, the series application method is proposed to improve the traditional integral method. On the trapezoidal integration method (is also called the bilinear transformation), a sinusoidal curve is used to improve the integral area. Therefore, the numerical compensation method during a sampling period can make the digitally sampled signal more closely match the originally analog response, so the new numerical integral is more accurate than the trapezoidal integration in the application of signal system. By the use of such a new technique, the original continuous-time system can be converted into an equivalent discrete-time one more precisely. In the application on digitalizing signal system, the newly generated digital transform is shown its better accuracy than the bilinear transform. Analysis of the mathematical transformation is given in this paper to show its adjustable characteristics for digital signal. An illustrated example is simulated on a real system via the developed technique to demonstrate its time-domain response.

在本文中，研究在數位信號系統中的有趣問題，包含取樣系統的取樣週期之大小與響應形態之不同。信號響應可由近似的三角函數級數展開描述，所展開的級數與取樣週期參數nT具有相關性。文中也研究提出一種級數應用的方法，改進了傳統的積分方法，針對梯形積分法（又稱為雙線性轉換），使用正弦波曲線去改善積分面積量。因此，在一個取樣週期中，用數值補償的方法，能夠使數位取樣信號與最原始的類比信號響應更為一致，此一新的數值積分法，相較於梯形積分法，更能精確地應用於信號系統中。利用此一新方法，可以更精確地將原始連續時間系統換成對等的數位時間數位系統。在數位信號系統的應用上，新產生的數位轉換比雙線性轉換呈現更佳的精確性。文中的數學轉換分析顯示了對數位信號的可調特性。

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