“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).

What I found was the Discrete Fourier Transform (DFT), which looks like this:

This formula, as anyone can see, makes no sense at all. I decided that Fourier must have been speaking to aliens, because if you gave me all the time and paper in the world, I would not have been able to come up with that.

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……” continued at: Understanding the Fourier transform (altdevblogaday.org)