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词汇 Elliptic filter
分类 英语词汇 英语翻译词典
释义

Elliptic filter

中文百科

椭圆函数滤波器

四阶低通椭圆滤波器的频率响应。

椭圆滤波器（Elliptic filter）又称考尔滤波器（Cauer filter），是在通带和阻带等波纹的一种滤波器。椭圆滤波器相比其他类型的滤波器，在阶数相同的条件下有着最小的通带和阻带波动。它在通带和阻带的波动相同，这一点区别于在通带和阻带都平坦的巴特沃斯滤波器，以及通带平坦、阻带等波纹或是阻带平坦、通带等波纹的切比雪夫滤波器。

一个低通椭圆滤波器的频率响应的幅度为：

G_n(\omega) = \left | H_n(j \omega) \right | = {1 \over \sqrt{1 + \epsilon^2 R_n^2(\omega)}}

其中R_n 是n 阶雅可比椭圆函数（Chebyshev rational functions）。

英语百科

Elliptic filter 椭圆函数滤波器

The frequency response of a fourth-order elliptic low-pass filter with ε=0.5 and ξ=1.05. Also shown are the minimum gain in the passband and the maximum gain in the stopband, and the transition region between normalized frequency 1 and ξ
A closeup of the transition region of the above plot.
An expanded view in the transition region of the above image, resolving the four poles and two double zeroes.

An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter with equalized ripple (equiripple) behavior in both the passband and the stopband. The amount of ripple in each band is independently adjustable, and no other filter of equal order can have a faster transition in gain between the passband and the stopband, for the given values of ripple (whether the ripple is equalized or not). Alternatively, one may give up the ability to adjust independently the passband and stopband ripple, and instead design a filter which is maximally insensitive to component variations.
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