I was reading A.E. Siegman's Fiber Fourier Optics paper and came across the following equation which was described as the DFT:enter image description here and I don't understand why it's that equation over the commonly known DFT:DFT and inverse DFT. I know it resembles the inverse one but I still don't get why it is it has the root of 1/N
(PS: sorry I don't know how to add equations I'm new)
If I understood correctly, the reason for confusion is that there's a root of $N$ instead of just $N$. If that's the case, I think, it's a matter of normalization. The idea is, basically, that "Fouried" function being "Inverse Fouried" should give the initial function. But this requires only the factors in both direct and inverse DFT to give $1/N$ being multiplied, which can be achieved in several ways: either direct has a factor of $1$ and inverse - the factor of $1/N$, or (for symmetry) both have $1/\sqrt N$. Check this source for more info starting from eq. 15 there (it's for FT, not for DFT though, but the idea is the same). I hope this helps.