中文说明：应用背景巴特沃斯被誉为解决“不可能”的数学问题。在这个时候，过滤器的设计需要相当数量的设计经验，由于理论的局限性，然后在使用。该过滤器在出版后30年内不常用。巴特沃斯说：“一个理想的电力滤波器不仅应该完全拒绝不必要的频率，但也应具有均匀的灵敏度为想要频率。这样一个理想的滤波器无法实现但巴特沃斯表明逐次逼近得到越来越多的数字正确值的过滤元素。在时间，过滤器产生在通带中的实质性的纹波，和元件值的选择高度互动。巴特沃斯表明低通滤波器可以设计其截止频率归一化，每秒1弧度，其频率响应（增益）是关键技术的Butterworth滤波器的频率响应是平坦（即没有涟漪）在通带和阻带中的卷向零。[ 2 ]时的对数Bode图，响应线性斜坡下向负无穷。一阶滤波器的响应滚下−每倍频程6分贝（20分贝每十−）（所有一阶低通滤波器具有相同的归一化频率回应）。一个二阶滤波器降低−12分贝每倍频程，一三阶在−18分贝等。Butterworth滤波器有单调变化的幅度函数ω，不像其他的过滤器在通带和/或在非单调纹波的类型阻带。用切比雪夫I型和II型滤波器、椭圆滤波器相比，Butterworth滤波器有一个缓慢的滚降，因此将需要实现一个特定的阻带规格高阶Butterworth滤波器，但更具有线性相位在通带中的响应比我/Ⅱ型和椭圆的带通带滤波器可以实现。
English Description：
Application background Butterworth had a reputation for solving "impossible" mathematical problems. At the time, filter design required a considerable amount of designer experience due to limitations of the theory then in use. The filter was not in common use for over 30 years after its publication. Butterworth stated that: "An ideal electrical filter should not only completely reject the unwanted frequencies but should also have uniform sensitivity for the wanted frequencies". Such an ideal filter cannot be achieved but Butterworth showed that successively closer approximations were obtained with increasing numbers of filter elements of the right values. At the time, filters generated substantial ripple in the passband, and the