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As title says, what is the low-pass filter that gives minimal transient response? By minimal transient response, I mean minimal settling time with reference to very tiny amount of divergence of steady-state values.

I am asking for analog case, but digital case would also be fine.

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  • $\begingroup$ In a digital filter it is simple - the length of the filter. This is inverse to the band pass width. In analog it is about the same and if you could implement a "time domain limited filter" than it is again limited to the time that the signal is "delayed" in the circuit. $\endgroup$ – Moti May 21 '15 at 3:04
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    $\begingroup$ I think it is difficult to give an exact answer to your question because the settling time depends on the Q factor of the filter (steepness of roll-off). The lower Q is (for a given cutoff frequency) the faster the settling time. $\endgroup$ – niaren May 21 '15 at 6:02
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As mentioned in the comments there is no unique answer to your question, because you're asking for a contradiction. A good low pass filter (i.e. one with a fast transition between pass band and stop band, and with high stopband attenuation) will exhibit a considerable transient response. On the other hand, a filter with a very smooth step response is worse as a frequency selective filter than other filters of the same order. However, a Bessel filter might be a good compromise between these two conflicting goals. It performs reasonably well as a low pass filter, and it has very little overshoot in its step response.

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