Approximation of the Fourier Series on a finite interval. Converts the signal from the time domain to the frequency domain

Input: windowed signal $x[n]... x[m]$

Output (for each frequency band): a complex number $X[k]$ representing the magnitude and phase of that frequency component in the original signal

We compute $X[k]$ with:

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