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Normally I'd just upvote and move on, but this is really fucking good. For example, I wish I could have seen something like that "Sine Wave Aliasing" page when I was learning this stuff, would have saved me a lot of confusion.

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Thanks! Let me know if there are other topics you'd like covered, or areas that need more explanation.

Another topic that has confounded me as much as FFTs are Quaternions.

Take a look at geometric algebra.

http://www.geometricalgebra.net/

http://en.m.wikipedia.org/wiki/Geometric_algebra

That's not quite the same, but worth reading up on anyway.

The quaternions are a subalgebra of geometric algebra. It's not quite the same in that it's strictly more general and, therefore, more broadly applicable.

I found this example by Steven Wittens to be remarkably well done: http://acko.net/blog/animate-your-way-to-glory-pt2/

See the section "Blowing up the Death Star" and note that there are 100 parts total.

"So that's quaternions, the magical rotation vectors."

This is great! I'd love to see sections on convolution, the Dirac delta function, and the continuous (possibly multi-dimensional) Fourier transform.

Seconded on convolution and the Dirac delta.

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