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|seen||Feb 5 at 22:48|
PhD student in machine learning.
Question about Fourier Transform
Your formulas are false. For example, the exponential terms in the integrals does not depend on the x, so the formulas are meaningless, they are not describing Fourier transform. True formula for the Fourier transform is, $$ F(\omega) = \int f(x) \exp(-i\omega x) dx$$ Corresponding second formula is, $$F(f) = \int f(x) \exp(-i 2 \pi f x) dx$$ You just define $\omega = 2 \pi f$, and this doesn't make difference in the general sense.