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Understanding the Fourier Transform

DerivedDFT

A great, non-expert explanation of the Fourier Transform by Stuart Riffle over at AltDevBlog.

A very long time ago, I was curious how to detect the strength of the bass and treble in music, in order to synchronize some graphical effects. I had no idea how to do such a thing, so I tried to figure it out, but I didn’t get very far. Eventually I learned that I needed something called a Fourier transform, so I took a trip to the library and looked it up (which is what we had to do back in those days).

Eventually, I was able to visualize how it works, which was a bit of a lightbulb for me. That’s what I want to write about today: an intuitive way to picture the Fourier transform. This may be obvious to you, but it wasn’t to me, so if you work with audio or rendering, I hope there’s something here you find useful.

Disclaimer: my math skills are pitch-patch at best, and this is just intended to be an informal article, so please don’t expect a rigorous treatment. However, I will do my best not to flat-out lie about anything, and I’m sure people will set me straight if I get something wrong.


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