双线性变换中的频率失真

Frequency Infidelity of Bi-Linear Transform

研究了双线性变换中的频率失真。对于二阶系统 ,提出了二阶差分方程的点阻效应的概念 ,导出了频率失真的误差关系式 ;对于一阶系统 ,通过考察 (- 3d B)通带边缘频率 ,推导出频率失真的误差关系式。这些关系式的正确性通过几个例子获得了验证。研究结果表明 ,双线性变换中的频率失真与采样频率和系统本身的特性有关 ,当系统特性确定后 ,增加采样频率 ,可以减少误差。实际应用中 ,对于二阶系统 ,采样频率应至少是系统固有频率的 15倍 ;对于一阶系统 ,应使采样频率和时间常数的乘积大于 2 。

The frequency infidelity of Bi Linear Transform is investigated in this paper. A new concept of 'Point Frequency Elimination Effect' is proposed for second order system, and the equation for quantitatively analyzing the frequency infidelity in fisrt order system is also given by investigating the frequency at 3dB band pass. Some examples are given to verify the correctness of these equations. The results obtained in the paper show that the frequency infidelity in Bi Linear Transform is related to sampling frequency and the characteristics of the system.The higher the sampling frequency is, the less the error there will be in a certain system. Thus it is proposed that the sampling frequency should be 15 times higher than the nature freuency of second order system, and the product of frequency and time constant of first order system should be more than 2 in order that the frequency infidelity is less in practical use.