fft_test():

  x:
[ 1.   2.   1.  -1.   1.5]

  y = fft(x):
[ 4.5       -0.j          2.08155948-1.65109876j -1.83155948+1.60822041j
 -1.83155948-1.60822041j  2.08155948+1.65109876j]

  z = ifft(y):
[ 1. +0.j  2. +0.j  1. +0.j -1. +0.j  1.5+0.j]