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So you got through 2 or 3 years of calculus at least a year of abstract algebra and probably 2 years of linear before you could understand what a Fourier transform was?

Color me skeptical

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Basically yes - but even now I'd have to admit I have no intuition for why the different "frequency" functions are orthogonal to each other.

this is more like 3 semesters of calculus, and 1 semester of linear

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