Can someone explain why there is an imaginary term when taking the fourier transform of sin(x)? I can see the math, but shouldn't the fourier transform of sin(x) be equivalent to $delta(x -1)$? I'm also not seeing how there are two deltas and especially why one of them is negative.
2026-03-26 08:00:43.1774512043
Meaning of the imaginary term in the Fourier transform of sin(x)
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The imaginary term indicates a phase shift.
It is a constant that can be taken out of the inverse fourier transform, which would give back a cosine, and then phase shift would be applied to the cosine to return a sine.