DFT Analysis equation

$X[k] = \sum_{n=0}^{N-1}x[n] e^{-2\pi j \frac{kn}{N}} , 0\leq k\leq N-1$

DFT Synthesis equation

$x[n] =\frac{1}{N} \sum_{k=0}^{N-1}X[k] e^{2\pi j \frac{kn}{N}} , 0\leq n\leq N-1$