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May 9, 2020 at 18:48 vote accept Dan Boschen
May 9, 2020 at 18:17 comment added Matt L. @DanBoschen: The proof is indeed given for a function of time, but nowhere does the proof rely on this fact. It is more that the application asked for sampling a function of time, hence this specialization. But the result is absolutely general, no matter if you sample in time, frequency, or space (or anything else).
May 9, 2020 at 18:04 comment added robert bristow-johnson not that Matt needs the boost in the rep, but +1 from me for saying it as it really is.
May 9, 2020 at 11:12 comment added Dan Boschen Hence my question as I thought perhaps given this predominant application to the time domain the same theorem may formally occur in other forms applicable to the frequency domain.
May 9, 2020 at 11:09 comment added Dan Boschen I thought that too (and that is applicable to all operations in either domain between time and frequency) but the original proof very clearly specifies the time domain and gives no mention to what I think would otherwise be obvious that it applies in either domain: web.archive.org/web/20100208112344/http://www.stanford.edu/… "Theorem 1: If a function contains no frequencies higher than cps, it is completely determined by giving its ordinates at a series of points spaced 1/2 seconds apart."
May 9, 2020 at 9:54 history answered Matt L. CC BY-SA 4.0