Question

Hey all, so I’m implementing the simple version of the discrete fourier transform in python for a class, but something strange is happening to my output and I have no idea why. For example if my input is [a,b,c,d] the values are getting scrambled like [a’,d’,c’,b’] with the head of the list in the same place, but the other values reversed. This is my code:

def DFT(pts, carr):
  t = time.clock()
  F =[0]*pts
  for k in range(pts):
    c = 2j*k*math.pi/pts
    for n in range(pts):
      F[k] += complex(carr[n]) * cmath.exp(n*c)
  t = time.clock()-t
  print(str(pts) + " point DFT finished in " + str(t) + "s")
  return F

It’s super simple, but for some reason it’s flipping the array around all willy-nilly and I have no idea why. Does someone know what’s going on here? I’m certain the input is in the right order.

Answer 1

I believe you’re missing a negative sign in the calculation of c (see this link).

With your code:

>>> DFT(4, [1, 2, 3, 4])
4 point DFT finished in 0.0310370227732s
[(10+0j), (-2.0000000000000004-1.9999999999999996j), (-2+9.797174393178826e-16j), (-1.9999999999999982+2.000000000000001j)]

With the missing negative sign:

>>> DFT(4, [1, 2, 3, 4])
4 point DFT finished in 4.17962941128e-05s
[(10+0j), (-2.0000000000000004+1.9999999999999996j), (-2-9.797174393178826e-16j), (-1.9999999999999982-2.000000000000001j)]