Find settling time for n-pole Butterworth, Chebychev etc

[741]

I'd like to juggle settling time vs sample rate and number of poles for an anti-aliasing filter. If I can use a formula, then I can enter lots of trial values into Excel.

For an 1 pole RC, we have Vc = V( 1 - e^(-t/(RC)) ) --> t = RC.ln(V/(V-Vc))

How do I calculate (ideally) or simulate in a short time the settling time of say a 4-pole 5Hz MFB Butterworth filter? (I guess the result would differ for say a Chebychev?)

If I use a simulator, would it speed the simulation up if I scale things to 5kHz then 'work back to 5Hz' somehow? Or, is this a false path because the simulator will automatically choose an appropriate timestep?

I'd like to know how long it takes a 1V step to settle to within (for instance) 1/1000 of a volt.

[rhb]

The settling time is the minimum phase waveform with the same frequency function.  I suggest using Octave rather than Excel.

A=filter amplitude spectrum

B=Hilbert transform of A

b = inverse FFT of B

b is the time domain response of the filter.