I am trying to get understand few things about DFT, from wikipedia:
$X_k=\sum_{n=0}^{N-1}x_ne^{-i2\pi\frac{k}{N}n}$, we have N numbers $x_0$ to $x_{N-1}$
Why there is $\frac{k}{N}*n$ in the exponent, in normal Fourier transform there was $e^{-i2\pi ft}$ where $t$ - time and $f$ - frequency, what is the meaning of $k$, does frequency is $\frac{k}{N}$ - if yes why also where is the time in which $x_n$ measured. I just can't see analogy between the equation for DFT and normal Fourier transform.
How do we specify the peroid of our data, we have discrete points, do we assume that if we would have 100 points then $T$ = 100?
I would be very grateful for answers.