E = cos(pi*linspace(0,15,16)/4)
E =
  Columns 1 through 7
    1.0000    0.7071    0.0000   -0.7071   -1.0000   -0.7071   -0.0000
  Columns 8 through 14
    0.7071    1.0000    0.7071    0.0000   -0.7071   -1.0000   -0.7071
  Columns 15 through 16
   -0.0000    0.7071

    F = fft(E)
ans =
  Columns 1 through 4
   0.0000            -0.0000 + 0.0000i   8.0000 - 0.0000i   0.0000 - 0.0000i
  Columns 5 through 8
   0.0000 - 0.0000i   0.0000 - 0.0000i   0.0000 - 0.0000i   0.0000 + 0.0000i
  Columns 9 through 12
  -0.0000             0.0000 - 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
  Columns 13 through 16
   0.0000 + 0.0000i   0.0000 + 0.0000i   8.0000 + 0.0000i  -0.0000 - 0.0000i

    ifft(F)
ans =
  Columns 1 through 7
    1.0000    0.7071    0.0000   -0.7071   -1.0000   -0.7071   -0.0000
  Columns 8 through 14
    0.7071    1.0000    0.7071    0.0000   -0.7071   -1.0000   -0.7071
  Columns 15 through 16
   -0.0000    0.7071