一種新型數值方法與其在數位系統之應用

A New Numerical Method and Its Application in Digital Systems

本文中，提出一種新型態的推導方法，以改進傳統的積分方法。針對梯型積分法（又稱為雙線性轉換），用補償的方法改善了積分面積量，使得新產生的數值積分比梯型積分法更加精確。利用此一新方法，可以更精準地將原始連續時間系統換成對等的數位時間數位系統。在數位化信號系統的應用上，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。舉出一個實際系統並用文中所提出的技巧模擬，展現在時域響應中。

This paper proposes a newly derived method to improve the traditional integral method. The trapezoidal integration method (also called the bilinear transform) compensates an improved integral area; therefore, the new numerical integral method is more accurate than the trapezoidal integration method. This new technique can be used to convert an original continuous-time system into an equivalent discrete-time system more precisely. In its application in a digital signal system, the newly generated digital transform has better accuracy than the bilinear transform does. An analysis of the mathematical transformation is given in this paper to show its adjustable characteristics for digital signal systems. An illustrated example was simulated on a real system using the developed method to demonstrate its time-domain response.