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**Continious FT of a rectangle is real valued but DFT of it is not!?**

Continious Fourier Transform of a rectangle with amplitude of 1 between [-u,u] is a real valued function (u is a positive number). Actually it is a sinc function.

However when I use discrete Fourier Transform (fft) I obtain complex numbers. I know they are complex conjugates but according to the formulas of continious and discrete versions of the transformation, the only difference should have been the dt factor. Am I missing something?