On the Transient Response of All-Pole Low-Pass Filters

From a study of filters of order ranging from one to five, it is conjectured that under the constraint of a fixed --3-dB bandwidth, an all-pole low-pass filter gives the best monotonic transient response when it has identical negative real poles. The term "best transient response" is used to mean least rise time and delay time and, in addition, the step response is not allowed to have a staircase shape. A partial proof of the conjecture is given, followed by a discussion of the time and frequency domain characteristics and realization of the identical negative real pole filter.