dft.py

import numpy as np

def dft(x):
    X = []
    N = len(x)
    for k in range(-N,N):
        re = 0
        im = 0
        for n in range(0,N):
            phi = (2*np.pi*k*n)/N
            re += x[n]*np.cos(phi)
            im -= x[n]*np.sin(phi)
        re = re/N
        im = im/N
        freq = k
        mag = abs(complex(re,im))
        phase = np.arctan(im/re)
        X.append([re,im,freq,mag,phase])
    return X