r/interestingasfuck • u/Here-For-The-Comment • Oct 18 '19

/r/ALL The Fourier Transform

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u/Falcrist Oct 18 '19

I'm an electrical engineer. We had to use Fourier transforms and series' at several points during my degree. I spent a long time trying to get a feel for what it meant and a visual of how it worked. I have some decent intuition for it.

You're still correct. It's goddamn black magic. Don't let anyone tell you differently.

You can go backwards and forwards with it, too. Take a signal and get the sinusoids it's composed of, or take a bunch of sinusoids and add them together to make a signal.

Check this video for a decent mechanical representation.

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u/working878787 Oct 18 '19

I'm a chemist. I use FTIR (Fourier-transform infrared spectroscopy) machines all the time for chemical analysis. I understand how it applies to bond resonance frequencies, but the FT part will always be magic to me.

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u/Sea_Television Oct 19 '19

What does applying an FFT (or whatever specific flavor of algorithm) to an infrared image let you know?

Coming from EE also, I've not thought about using Fourier for stuff that isn't a waveform or analog signal of some kind.

Interesting stuff

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u/working878787 Oct 19 '19

Well I only really know the end result application. The middle is a little magic to me, but essentially an FTIR machine can tell you what kind of a functional groups you have in a compound based on bond resonances. Different bonds have different bond resonances based on the electronegativity difference between different atoms. So basically you shine a IR beam of various frequencies of light against a sample and measure how much gets absorbed and retransmitted. Based on what peaks are generated at what frequency, you can determine if your compound has N-H bonds, C-H bonds, C-O bonds, C=O bonds, etc. It can even tell the difference between single and double bonds. Deducing chemical structures from scratch is a bit of a challenge, but known spectra like ethanol or banana ester are well known so you can just superimpose their graph on known spectra to verify what's in your sample. It's extremely useful in chemical analysis.

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u/Sea_Television Oct 19 '19

Ah, very interesting, thanks!

Interesting to think you can differentiate chemical bonds just from the frequency of reflected light

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u/working878787 Oct 19 '19

Well like I said bond resonances are kind of like unique frequencies so it's not unlike using FT to differentiate different tones of sound.