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Re: Problems with FFT and IFFT


From: Sascha Berkenkamp
Subject: Re: Problems with FFT and IFFT
Date: Tue, 28 Feb 2006 20:13:55 +0100
User-agent: Mutt/1.5.11+cvs20060126

* John W. Eaton <address@hidden> [28.02.2006 17:52]:
> What kind of hardware?  I see imaginary parts, but all less than
> eps.

I use x86, Pentium Centrino 1.6 GHZ, Octave from Debian Etch

>    octave_config_info ("FFTW_LIBS")

octave:21>  octave_config_info ("FFTW_LIBS")
ans = -lfftw3

Some of the values are greater than eps
octave:22> eps
eps =  2.2204e-16

octave:23> imag(x2)
ans =

 Columns 1 through 8:

    0.0000e+00    3.5175e-17    1.1061e-16    6.6476e-17    2.1199e-16
    -2.4203e-17    2.0483e-16    2.5125e-17

 Columns 9 through 16:

   -1.9568e-16   -1.3944e-16    1.0716e-16   -3.9844e-17   -9.0520e-17
   2.5194e-16    1.0905e-18   -1.6137e-16

 Columns 17 through 24:

   -5.0008e-17    3.7599e-17    6.8233e-17   -7.3672e-17    2.1367e-16
   3.0135e-17   -1.1130e-16   -4.6083e-17

 Columns 25 through 32:

    2.5070e-17   -3.2290e-16    3.4958e-17   -8.9096e-17   -1.4279e-16
    1.3788e-16    5.2801e-17    2.9702e-17

 Columns 33 through 40:

   -1.7758e-16    7.6944e-19    2.3255e-16    1.5679e-16   -2.0947e-17
   2.0342e-16   -1.9384e-16   -1.2851e-16

 Columns 41 through 48:

    1.9127e-16    3.5370e-17   -2.0086e-18    1.1304e-17    1.3220e-16
    -4.5291e-18   -9.9986e-17   -1.6011e-16

 Columns 49 through 56:

   -3.9844e-17    6.3589e-17   -1.0564e-16   -3.0778e-17    1.4462e-16
   -4.0874e-17    8.2015e-17    1.7684e-16

 Columns 57 through 64:

   -5.7632e-17    5.4866e-18   -4.8098e-17   -3.8728e-17   -8.8911e-17
   9.4316e-17   -7.3907e-18   -9.4484e-18

 Columns 65 through 72:

   -3.2554e-16    0.0000e+00   -1.1167e-16   -1.0787e-16    3.0963e-17
   7.2214e-17    1.0869e-16    2.7486e-17
 Columns 73 through 80:

   -3.6979e-17   -2.3208e-17    1.7468e-17   -9.6645e-17    2.5633e-16
   -3.9809e-17    1.2463e-17    3.3627e-17

 Columns 81 through 88:

    7.7609e-17   -8.7662e-17    2.7347e-17    3.0778e-17   -4.0610e-17
    5.7000e-17    1.9934e-16   -2.0947e-17

 Columns 89 through 96:

   -2.4703e-16    4.5723e-17    1.1818e-16    8.1443e-18   -4.6655e-18
   1.5679e-16    7.6130e-17   -4.0610e-17

 Columns 97 through 101:

   -1.9494e-16   -1.0285e-16   -8.9592e-17   -1.5124e-16   -6.7643e-17


But I think that the values before the transformation and after the
retransformation are not the same:

octave:27> real(x) 
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

....

octave:27> real(x2)
Columns 1 through 8:

    4.6168e-17    5.8779e-01    9.5106e-01    9.5106e-01    5.8779e-01
    -7.0351e-17   -5.8779e-01   -9.5106e-01

 Columns 9 through 16:

   -9.5106e-01   -5.8779e-01   -3.1658e-16    5.8779e-01    9.5106e-01
   9.5106e-01    5.8779e-01   -3.5175e-17

 Columns 17 through 24:

   -5.8779e-01   -9.5106e-01   -9.5106e-01   -5.8779e-01   -2.1105e-16
   5.8779e-01    9.5106e-01    9.5106e-01

Must I set all values smaller than eps to zeros?


Sascha

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