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I assume that the sampling rate is w_s = 2w_max if we have an ideal low-pass filter that nulls frequencies whose absolute value is higher than that of w_max. Therefore, that the only reason for oversampling is to compensate for the imperfect filters whose magnitude at the stop-band isn't exactly 0, etc.

Consequently, one should oversample to limit the unwanted effects of the imperfect filters. But how much? What's a "good" sampling rate for a given filter of a given order e.g. the Butterworth of order 7?

Thanks!

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There are other reasons for over-sampling. First is if you want to reconstruct the signal back into the analogue domain you have an easier job designing the DAC output filter. Remember that the process of digitization does "corrupt" the signals closer to half sample rate and that corruptions lowers the higher frequency amplitudes by a few dB - the reconstruction filter needs to be designed more carefully the closer you run to the half sample rate.

Another reason might be the ability to get "process gain" - this can significantly reduce the SNR incurred during the digitization process and improve overall SNR. Your question....

What's a "good" sampling rate for a given filter of a given order e.g. the Butterworth of order 7?

... is unanswerable based on what I've said above.

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