[HN Gopher] The Fourier Uncertainty Principles [pdf] (2021)
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The Fourier Uncertainty Principles [pdf] (2021)
Author : mindcrime
Score : 45 points
Date : 2024-09-03 17:23 UTC (5 hours ago)
(HTM) web link (math.uchicago.edu)
(TXT) w3m dump (math.uchicago.edu)
| gballan wrote:
| There is an approachable explanation in [1], chapter 16
| ("Duration-bandwidth relationships and the uncertainty
| principle"), that says that the product of rise-time and
| bandwidth of a signal must be greater than some minimum.
|
| [1] Siebert, W. M. (1986). Circuits, Signals, and Systems.
| McGraw-Hill.
| peter_d_sherman wrote:
| >"The most popular use of Fourier uncertainty principles is as a
| description of the natural _tradeoff_ between the _stability_ and
| _measurability_ of a system "
|
| Related:
|
| https://en.wikipedia.org/wiki/Complementarity_(physics)
| wyager wrote:
| I have read a lot of documents on ncatlab and other places to try
| to pin down a coherent model of the physical role of planck's
| constant in fourier transforms on physical systems. I understand
| that it often serves as the scale factor for embedding the
| integers into the reals, but it's not totally clear to me what
| its role is in physical pontryagin duality/fourier transforms.
| It's some kind of volume in phase space, but where does that
| volume come from? For a constant like c, we have the narrative "c
| is the ratio of unit lengths in time and space", but I have not
| yet found a good narrative about the meaning of h that works for
| fourier transforms. Would appreciate any articles on the matter.
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