Hello Evryone!

I've noticed this about Fourier transform.

Suppose we're convolving a single tone sinusoid with a sinc function, namely [TEX]\sin(at)/\pi t[\TEX], then, by taking their CTFT, we get a rect multiplied with 2 pure imaginary deltas. Now what's the significance of our transform being imaginary, not just in this case? Does it just come out of the math involved?

Thanks!