时域测量中高斯低通滤波器的有理逼近设计方法

用时域法测量电子设备的幅频特性需要高斯低通滤波器产生阶跃信号.高斯滤波器是一种理想的时域滤波器,是非因果系统,可以采用逼近的思想加以设计实现.采用有理逼近方法,对高斯滤波器幅频响应进行泰勒展开,由泰勒展开式逼近高斯滤波器幅频特性.根据模拟滤波器幅度平方设计方法,由展开式左半平面极点建立逼近滤波器模型,随着逼近阶次的增加...

Rational Approximation Implementation Approach for Gaussian Low-pass Filter in Time Domain Measurement

The step signal produced by Gaussian low-pass filter is required to measure the amplitude frequency characteristics of electronic equipment by time domain method.Gaussian filter is an ideal time domain filter and a noncausal system,which could be implemented by approximation theory.In this paper,the amplitude-frequency response of Gaussian filter is expanded into Taylor series by rational approximation method and the Taylor expansion approximates the amplitude-frequency characteristics of Gaussian filter.Based on the square amplitude design method of analog filter,the approximation filter is established by the left half plane poles of the expansion.With the increase of the order,approximation precision will improve and the maximum amplitude error of six order system reaches 1.5%.The approximation filter could be decomposed into a series of second order systems and a first order system.The circuit for second order system is designed by universal model,the first order system is RC filter and the analog Gaussian approximation filter is established after these unit circuits connect in series.Furthermore,the relation table of the poles of Taylor expansion and the bandwidth constant α is established.The poles could be determined through looking up the table,which strengthens the practicability of this method.