3 ms·
Indeed, the uncertainty principle arises directly from the Shannon-Nyquist sampling theorem! [0] [0] https://arxiv.org/abs/1108.3135 https://arxiv.org/abs/1108
by lidHanteyk 7y ago
Indeed, the uncertainty principle arises directly from the Shannon-Nyquist sampling theorem! [0]
[0] https://arxiv.org/abs/1108.3135 https://arxiv.org/abs/1108.3135
- blattimwind 7y agoYou don't need to do a fourier transform to measure a frequency, though. It doesn't really need anything special to measure the frequency of a 440 Hz tone to six digits or so given a single cycle. With some trickery you can get right down to 10-20 ps resolution, which would give you approximately eight digits from a single 440 Hz cycle. There is no frequency-domain effect here that would prevent you from measuring the time interval of a single cycle more accurately, except that it simply gets difficult on an electrical level when we are talking about resolving sub-ps intervals.
- Misdicorl 7y agoMeasuring the half wave length of some physical process is literally performing the Fourier transform and pulling out the dominant coefficient
- vermarish 7y agoI think we're interpreting the link you provided differently. The way I read it, the author is taking the analogy between the Fourier Uncertainty and the Heisenburg Uncertainty and extending it to a similar analogy between the Nyquist Theorem and Brillouin Zones.