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This is what made it click for me, can recommend it:

3Blue1Brown -- But what is the Fourier Transform? A visual introduction.

https://www.youtube.com/watch?v=spUNpyF58BY

That video did the same for me. I also like the reducible video for Fast Fourier Transforms as well as the Veratasium piece that shares some fun history.

Reducible - FFTs the most ingenious algorithm ever https://youtu.be/h7apO7q16V0 Veritasium - The Most Important Algorithm of All Time https://youtu.be/nmgFG7PUHfo

100%,those are excellent, but didn't exist when it first clicked for me. Being in university now must be great having such access to explanations that really get to the root of a concept

The FFT is something I still can't quite grok, for some reason.

I had the same problem. Then I took a math course where we covered the general fourier transform and it made way more sense. An the FFT is the result of a simplifying transformation based on discrete regularly spaced points and that's really opaque from the other side.

I guarantee that you will be able to "grok" it from this book: https://news.ycombinator.com/item?id=34207380

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