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> best semi-intuitive, non rigorous explanation [...] signal correlation in the time domain [...] basically performing correlation on the signal for all the pos
by ajross 4y ago
> best semi-intuitive, non rigorous explanation [...] signal correlation in the time domain [...] basically performing correlation on the signal for all the possible sines at different frequencies
That's only going to make sense for someone who understands your jargon usage of "correlate", and who groks that integrals of sine curves are orthogonal under addition. That's precisely the hard part the linked explanation is trying to explain.
If you've already gotten that far then the DFT is just calculator math.
- voidhorse 4y agoTrue! Though tbh, I did not even know that property of integrals, since I've studied this stuff only in the discrete realm. At the totally basic level, another thing that I think can really trip people up and that a lot of texts are not clear about is that the transform is about moving between representations and that we're not actually transforming anything. Not enough maths texts take the time to explain how the representation connects up with the objects we wish to study and how there are multiple possible ways to represent them, and in some cases, like Fourier, useful ways to "translate" between different representations.