agh! look who it is again, ye ole jester of the night! good day my sir, you've sminkledorffed me yet again!
A Fourier Transform can be seen as a continuous generalization of a Fourier Series.
That is, we make the replacements:
(1) ∑ → ∫
(2) c_k → c(k)
The function c(k) is called the "spectral function", and tells us the distribution of wavelengths that make up f(x)pic.twitter.com/CsjScG8ohX
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For some reason mathematicians seem to disapprove, but I like to introduce the Fourier transform as a change of basis in L2.
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The language of bases quickly gets unbearable in infinite dimensions. But the approach itself can be very useful indeedhttps://twitter.com/ValFadeev/status/1130245090356748289?s=09 …
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It's not only an analogy, it's a true generalization, if you do Fourier transform over locally compacts group, you can get back Fourier Series
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You can even get discrete Fourier transform just by using a finite group
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I suppose it has confusion between 'k' and 'n' in the discrete version?
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