摘要
O.Herrmann 通过分析切比雪夫解析解,推导出估算低通滤波器阶数 N的公式(简称 Herramnn 公式),该公式揭示了截止频率、阶数和峰值误差之间的关系.本文的研究是在 Herrmann 公式的基础上,分析了低通滤波器与高通、带通、带阻滤波器在频带上的关系,利用频带变换的方法,将 Herrmann公式推广到高通及对称带阻滤波器阶数 N 的估算中,并根据最佳逼近原理和Remez 算法,研制出一般选频滤波器等波纹逼近设计的具体算法程序.
O.Herrmann deduced the equation for estimating for,order N of Low-Pass filters by artalyzing Chebyshev solution 'Herrmann equation',Herrmann equ- ation reveals the relationship between the cut-off frequency,the order and the peak error.This paper is based on Herrmann equation,analyses the relationship between the.low-pass and high-pass,band-pass band-stop filters in frequency- band,introduces Herrmann equation to the estimation of the order N of high- pass,symmetrical band-pass and symmetrical band-stop filters by way of frequency-band transmission,and develops the algorithm program for selective filter design.
关键词
滤波器
Herrmann公式
频带变换
Herrmann equation
band-stop filter
transforming frequencyband
peak error
cut-off frequency
