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In practice it doesn't really matter. Most good converters have pretty sharp cutoffs on their anti-aliasing filters, so any aliasing is severely reduced when mixed back in to the converter. Sure an aperiodic signal needs infinite bandwidth to 'accurately' represent it, but you're quickly below the noise floor.


Sure. And having that 2+ kHz headroom surely helps. Still, it is a bit jarring to almost never see reconstruction filter mentioned (except for sigma delta, where you simply cannot ignore it), and always see appeals to Nyquist theorem as a mathematical proof, even though it does not apply.

Taking the opportunity, how is the math called that actually does apply to this case?


Every ADC/DAC used in audio in existence has an anti-aliasing filter, though. The Xiph video even talks about band-limiting signals with the 21 kHz cutoff filter he shows as the example.

It's not talked about, largely, because modern circuit designs already have great anti-aliasing filters that have quite sharp rejection curves.




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