Re: Problems with FFT and IFFT

[Keith Goodman]

Should the last line in your example be imag(x2)? Matlab gives zero
and Octave gives eps:

>> eps
eps =  2.2204e-16
>> imag(x2)
ans =

 Columns 1 through 9:
    0.0000e+00   -2.6382e-17    1.8793e-17   -1.1891e-16   -8.2877e-17
  -3.6586e-18    3.9801e-17    2.2479e-16   -6.5572e-17
 Columns 10 through 18:
   -5.4014e-17   -1.4229e-17   -2.0445e-17   -1.0258e-16    7.1639e-17
   2.3891e-18   -1.0553e-16   -3.6597e-17    1.4245e-17
 Columns 19 through 27:
   -9.8162e-17   -2.1105e-16   -8.5868e-17   -9.7389e-17    5.3450e-17
  -8.7306e-17   -1.0856e-16   -1.7588e-17    6.4697e-17
 Columns 28 through 36:
   -6.6063e-17   -7.0988e-18    9.6732e-17    1.2092e-16   -1.5921e-17
   5.4349e-18    1.0205e-16   -5.5355e-17   -1.8688e-16
 Columns 37 through 45:
   -7.2788e-17   -6.9880e-17   -7.0351e-17   -7.2984e-17    1.0605e-16
  -7.0351e-17   -1.4646e-17   -1.7588e-17    2.5443e-17
 Columns 46 through 54:
   -2.3834e-16    8.4440e-19   -2.9011e-18   -9.3385e-17    1.1913e-16
  -1.3026e-16   -2.8030e-17   -5.5824e-17   -4.1861e-17
 Columns 55 through 63:
    1.3379e-16   -1.5866e-17    2.5757e-16   -1.4229e-17    3.5175e-17
   2.2798e-17    1.3191e-16   -3.0879e-18    5.4349e-18
 Columns 64 through 72:
   -1.0553e-16    9.2741e-17    1.1065e-16    1.5094e-16   -3.0456e-17
  -7.5940e-17    6.0831e-17   -3.7655e-17   -5.0565e-17
 Columns 73 through 81:
   -7.0351e-17   -1.4254e-17    5.1041e-17    3.8263e-17    3.5175e-17
   6.0878e-17    4.8140e-17    2.9795e-17    5.6268e-18
 Columns 82 through 90:
    1.5739e-16    1.8467e-16    2.2967e-16    1.0479e-16   -2.3657e-17
   1.2311e-16   -9.0447e-17   -1.0048e-16    1.4024e-16
 Columns 91 through 99:
    9.2517e-18   -5.7259e-17   -6.6003e-17    2.3036e-16   -1.3951e-16
  -9.1052e-17   -3.6107e-17    6.7637e-17    5.2262e-17
 Columns 100 and 101:
    2.4331e-17    8.7938e-18



On 2/28/06, Keith Goodman <address@hidden> wrote:
> On 2/28/06, Sascha Berkenkamp <address@hidden> wrote:
> > Hi,
> >
> > I've got a simple problem with the FFT and the IFFT function.
> > I have got one function from matlab with both functions in it. But I
> > will not get the same results. So I started with testing on simple
> > task.
> > I have got a signal, transform it to the frequenz-domain and then I
> > transform it back to the time-domain.
> > Generally after transforming the signal shout be the same than the
> > input signal.
> > So my input signal (x) has no imag-part. So my retransformed signal
> > shoud have no imag-part, too.
> >
> > fs = 0:0.1:10;
> > x = sin(2*pi*fs);
> > real(x)
> > imag(x)
> > X  = fft(x);
> > x2 = ifft(X);
> > real(x)
> > imag(x)
> >
> > But in my octave version (octave 2.1.72 from debian etch) the
> > imag-part of the retransformed signal is not zero.
> >
> > When I put the code into matlab, everything is okay: no imag-part
> > after retransforming into the time-domain.
> >
> > Sascha
>
> Here's what I get (no imaginary part; I get the same result in 2.1.72):
>
> $ octave
> Octave 2.9.4 Forge 20050613
> >> fs = 0:0.1:10;
> >> x = sin(2*pi*fs);
> >> real(x)
> ans =
>
>  Columns 1 through 12:
>    0.00000   0.58779   0.95106   0.95106   0.58779   0.00000  -0.58779
>  -0.95106  -0.95106  -0.58779  -0.00000   0.58779
>  Columns 13 through 24:
>    0.95106   0.95106   0.58779   0.00000  -0.58779  -0.95106  -0.95106
>  -0.58779  -0.00000   0.58779   0.95106   0.95106
>  Columns 25 through 36:
>    0.58779   0.00000  -0.58779  -0.95106  -0.95106  -0.58779  -0.00000
>   0.58779   0.95106   0.95106   0.58779   0.00000
>  Columns 37 through 48:
>   -0.58779  -0.95106  -0.95106  -0.58779  -0.00000   0.58779   0.95106
>   0.95106   0.58779   0.00000  -0.58779  -0.95106
>  Columns 49 through 60:
>   -0.95106  -0.58779  -0.00000   0.58779   0.95106   0.95106   0.58779
>   0.00000  -0.58779  -0.95106  -0.95106  -0.58779
>  Columns 61 through 72:
>   -0.00000   0.58779   0.95106   0.95106   0.58779  -0.00000  -0.58779
>  -0.95106  -0.95106  -0.58779  -0.00000   0.58779
>  Columns 73 through 84:
>    0.95106   0.95106   0.58779   0.00000  -0.58779  -0.95106  -0.95106
>  -0.58779  -0.00000   0.58779   0.95106   0.95106
>  Columns 85 through 96:
>    0.58779  -0.00000  -0.58779  -0.95106  -0.95106  -0.58779  -0.00000
>   0.58779   0.95106   0.95106   0.58779   0.00000
>  Columns 97 through 101:
>   -0.58779  -0.95106  -0.95106  -0.58779  -0.00000
>
> >> imag(x)
> ans =
>
>  Columns 1 through 42:
>   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
> 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
>  Columns 43 through 84:
>   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
> 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
>  Columns 85 through 101:
>   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
>
> >> X  = fft(x);
> >> x2 = ifft(X);
> >> real(x)
> ans =
>
>  Columns 1 through 12:
>    0.00000   0.58779   0.95106   0.95106   0.58779   0.00000  -0.58779
>  -0.95106  -0.95106  -0.58779  -0.00000   0.58779
>  Columns 13 through 24:
>    0.95106   0.95106   0.58779   0.00000  -0.58779  -0.95106  -0.95106
>  -0.58779  -0.00000   0.58779   0.95106   0.95106
>  Columns 25 through 36:
>    0.58779   0.00000  -0.58779  -0.95106  -0.95106  -0.58779  -0.00000
>   0.58779   0.95106   0.95106   0.58779   0.00000
>  Columns 37 through 48:
>   -0.58779  -0.95106  -0.95106  -0.58779  -0.00000   0.58779   0.95106
>   0.95106   0.58779   0.00000  -0.58779  -0.95106
>  Columns 49 through 60:
>   -0.95106  -0.58779  -0.00000   0.58779   0.95106   0.95106   0.58779
>   0.00000  -0.58779  -0.95106  -0.95106  -0.58779
>  Columns 61 through 72:
>   -0.00000   0.58779   0.95106   0.95106   0.58779  -0.00000  -0.58779
>  -0.95106  -0.95106  -0.58779  -0.00000   0.58779
>  Columns 73 through 84:
>    0.95106   0.95106   0.58779   0.00000  -0.58779  -0.95106  -0.95106
>  -0.58779  -0.00000   0.58779   0.95106   0.95106
>  Columns 85 through 96:
>    0.58779  -0.00000  -0.58779  -0.95106  -0.95106  -0.58779  -0.00000
>   0.58779   0.95106   0.95106   0.58779   0.00000
>  Columns 97 through 101:
>   -0.58779  -0.95106  -0.95106  -0.58779  -0.00000
>
> >> imag(x)
> ans =
>
>  Columns 1 through 42:
>   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
> 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
>  Columns 43 through 84:
>   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
> 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
>  Columns 85 through 101:
>   0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
>
> >>
>



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