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?



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Usually, one has a noise floor requirement. So one can set the sampling rate to over twice the frequency where the filter response (and/or spectrum in the input) goes below this desired noise floor.


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