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I'll leave the discussion of how embellished this post/blog/exercise of MIT Comp Sci in 1 year is to other comments. But! The explanation of Fourier transforms from Scott's notes (http://www.scotthyoung.com/mit/fourier.pdf) is one of the must succinct ones I've read. I've always understood what the transform does, but the nitty gritty on how the equation works was awesome

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Yes, it was interesting to see it labelled out like that. I liked to think of the transform as a cross-correlation. You take a wave of a particular frequency (f) and cross-correlate it with your signal s(t) across all time. The fourier coefficients are the results of the cross-correlation, telling you how much of each frequency you have in your signal.

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