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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: 0.212s | source
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Salgat ◴[04 Sep 25 22:35 UTC] No.45133006[source]▶
Always blew my mind that every signal can be recreated simply by adding different sine waves together.
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incognito124 ◴[04 Sep 25 22:44 UTC] No.45133091[source]▶
Back in my uni days I did not get why that works. Why are sine waves special?

Turns out... they are not! You can do the same thing using a different set of functions, like Legendre polynomials, or wavelets.

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1. MontyCarloHall ◴[04 Sep 25 23:21 UTC] No.45133348[source]▶
>Turns out... they are not! You can do the same thing using a different set of functions, like Legendre polynomials, or wavelets.

Yup, any set of orthogonal functions! The special thing about sines is that they form an exceptionally easy-to-understand orthogonal basis, with a bunch of other nice properties to boot.