Transition between a flat magnitude and a sharp cut-off lowpass filter

A Butterworth lowpass filter provides excellent flatness around ω = 0 but the cut-off rate is low. Recently improvements to the cut-off rate have been made by introducing one ripple near the band edge. This paper offers a generalized design technique such that any degree of trade-offs between flat magnitude around ω = 0 and sharp cut-off at the band edge can be obtained while keeping the ratio of the reflected power to the transmitted power at minimum. © 1979 Taylor and Francis Group, LLC.