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What Is the Fourier Transform?

(www.quantamagazine.org)
474 points rbanffy | 1 comments | 04 Sep 25 22:11 UTC | HN request time: 0.197s | source
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eric-burel ◴[05 Sep 25 11:45 UTC] No.45137452[source]▶
What always bothered me when trying to "feel" Fourier transforms is that to compute the oscillations, you need to wait some time. Mathematically, the transformation includes computing integrals. So it's tricky to understand how you compute the Fourier decomposition for a stream. Illustrations always show the whole signal over time but in real life you get the signal progressively. I'd be eager to read more on this.
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1. jeremyscanvic ◴[05 Sep 25 12:28 UTC] No.45137735[source]▶
The keyword you're looking for is time-frequency analysis and the main associated tool is the short-time Fourier transform(s). This is the theory underlying spectrograms and all those niceties!