时域测量中高斯低通滤波器的有理逼近设计方法  

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

作　　者：许景波[1,2] 袁怡宝[3] 刘泊[1,2] 林海军[1,2] 李建新[1,2] 

机构地区：[1]哈尔滨理工大学测控技术与通信工程学院,哈尔滨150080 [2]测控技术与仪器黑龙江省高校重点实验室,哈尔滨150080 [3]哈尔滨工业大学自动化测试与控制系,哈尔滨150001

出　　处：《固体电子学研究与进展》2011年第6期553-558,共6页Research & Progress of SSE

基　　金：黑龙江省教育厅科学技术研究资助项目(11541053)

摘　　要：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,逼近精度将提高,六阶系统逼近最大幅度偏差达到了1.5%。将逼近滤波器分解成一系列二阶系统和一阶系统,对于二阶系统采用通用二阶系统模型进行电路设计,对于一阶系统采用一阶RC滤波器,最后将这些单元电路串联,组成模拟高斯逼近滤波器。建立了各阶泰勒展开式极点与滤波器带宽常数α的对应关系表,通过查表即可确定极点,增强了本方法的实用性。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 approxi- mation 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 de- composed into a series of second order systems and a first order system. The circuit for second or- der system is designed by universal model, the first order system is RC filter and the analogGaussian approximation filter is established after these unit circuits connect in series. more, the relation table of the poles of Taylor expansion and the bandwidth constant a lished. The poles could be determined through looking up the table, which strengthens ticability of this method. Furtheris estabthe prac-tieability of this method.

关 键 词：高斯滤波器 有理逼近 泰勒展开式 幅度平方设计法 

分 类 号：TN713[电子电信—电路与系统]