A new kind of the allpole lowpass filter functions with Chebyshev behaviour in the passband is derived by minimizing the passband insertion loss. The ripple parameter $\epsilon$, commonly used to control the attenuation at the cutoff frequency, in proposed approximation is used as a degree of freedom by which the passband attenuation can be controlled, while keeping the attenuation at the cutoff frequency equal to 3 dB. The approximation method relies on solving the nonlinear equation such that the area under the filter characteristic function in passband is minimized. Obtained filters, called Optimum Chebyshev filters, exhibit minimum insertion loss and maximum cutoff slope. Filter polynomial coefficients and the elements values for the LC ladder implementation are tabulated for filter degrees from 3 to 11.

Comparison of the Optimum Chebyshev and Least Square Monotonic filters is also discussed in the paper, since both filters are developed subject to the minimum reflected power in the passband; the first with the equiripple and the second with the staircase (monotonic) behavior in the passband. It is also revealed that the Optimum Chebyshev approximation can be considered as the optimal solution among the class of filters whose passband response is bound to be a staircase.

通过最小化通带插入损耗，可以得出一种在通带中具有切比雪夫特性的新型全极低通滤波器功能。纹波参数$\epsilon$通常用于控制截止频率处的衰减，在建议的近似中用作自由度，通过该自由度可以控制通带衰减，同时保持截止频率处的衰减等于3 dB。近似方法依赖于求解非线性方程，以使通带中滤波器特性函数下的面积最小。获得的滤波器称为Optimum Chebyshev滤波器，具有最小的插入损耗和最大的截止斜率。将滤波器阶数从3到11的滤波器多项式系数和LC梯形图实现的元素值制成表格。

本文还讨论了最佳切比雪夫滤波器和最小二乘单调滤波器的比较，因为这两种滤波器都是在通带内具有最小反射功率的基础上开发的。第一个具有等波纹，第二个具有通带中的阶梯（单调）行为。还揭示了最佳切比雪夫近似可以被认为是其通带响应必然是阶梯的滤波器类别中的最佳解决方案。