# What is the Fourier Transform and what is it good for?

Originally published at: https://boingboing.net/2018/01/29/what-is-the-fourier-transform.html

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Use them almost daily solving 3d structures of proteins.

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I remember using them with a/c compressors when I was an intern at GM back in the 80s. Those transient vibrations can either cause unpleasant harmonics in the rest of the car, or really screw up the compressor running smoothly.

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Same, except I’m just turning time-domain audio data into frequency-domain so I can see what the sound looks like.

Obligatory XKCD.

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A mental breakthrough came for me when I realised that the Fourier basis is just one of many bases, and neither it nor the pixel basis (or delta function basis - the usual PCM kind of basis) have any claim over being special. They’re just different representations of the information.

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FFTs are tricky. I have spent most of the last couple years teaching a CHAMP-WB + A25G digitizer and FPGA board set to be a pair of FFT spectrometers with 5 GHz bandwidth, with continuous back-to-back output of spectra, for a radio telescope. (I cheated and let a company in England write the FFT code itself; I just integrated it with all the other stuff needed.)

You can’t do that in Borland Basic.

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Godamit, I knew I was doing something wrong!

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Yep, just like polar coordinates or rectangular - pick the one that works for the job!

Now, if I can just get people to understand the volts/amps duality in electronics. It makes it so much easier for explaining optoelectronics when I say 1 photon = 0.55 electrons (well, actually conversion at 55% efficiency) - the volts are often meaningless!

p.s. If the signal is loud enough, like in resonance, it’s easy to just use a scope in time-domain mode.

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It is a little special, if you like harmonic oscillators.

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Same here, for MRI. The spatial encoding in MRI is a bit odd, so the (time domain) signal you record is in Fourier space. You have to Fourier transform it to get a picture of whatever appendage you stuck in the machine.

Following nixiebunny, we (almost) all use an FFT to achieve our Fourier transforms, which is a beautiful algorithm.

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Doing it on your new-fangled electrical compooters, haw? Kids these days, eh?

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This is what electrical engineering basically turns into.

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