Discrete Fourier Transform (DFT)
Definition of DFT
DFT
$ X[k] = \sum_{n=0}^{N-1}{x[n]e^{-j \frac{2{\pi}}{N}kn}}, for \mbox{ }k = 0, 1, 2, 3, ..., N-1 $
IDFT
$ x[n] = \frac{1}{N}\sum_{k=0}^{N-1}{X(k)e^{j \frac{2{\pi}}{N}kn}}, for \mbox{ }n = 0, 1, 2, 3, ..., N-1 $
