I Continious FT of a rectangle waveform is real valued, but the DFT of it is not?

[truva]

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?

 

[anorlunda]

The DFT returns both amplitude and phase information.

 

[rude man]

It's a matter of picking your time axis.
If your rectangular function is defned from 0 to 2u instead of -u to u you will get a complex number too.