[Numpy-discussion] second 2d fft gives the same result as fft+ifft

David Goldsmith d_l_goldsmith@yahoo....
Tue Jun 9 13:06:50 CDT 2009


Sorry, I meant:

      Im(iFT(FT(f))) = Im(FT^2(f)), Re(iFT(FT(f))) != Re(FT^2(f))

DG

--- On Tue, 6/9/09, David Goldsmith <d_l_goldsmith@yahoo.com> wrote:

> From: David Goldsmith <d_l_goldsmith@yahoo.com>
> Subject: Re: [Numpy-discussion] second 2d fft gives the same result as fft+ifft
> To: "Discussion of Numerical Python" <numpy-discussion@scipy.org>
> Date: Tuesday, June 9, 2009, 11:01 AM
> 
> --- On Tue, 6/9/09, Matthieu Brucher <matthieu.brucher@gmail.com>
> wrote:
> 
> > Hi,
> > 
> > Is it really ?
> > You only show the imaginary part of the FFT, so you
> can't
> > be sure of
> > what you are saying.
> 
> Indeed, is there not a "label" for a function f which
> satisfies 
> 
>      Im(iFFT(f)) = Im(FFT^2(f)),
> Re(iFFT(f)) != Re(FFT^2(f))?
> 
> (And similarly if Im and Re roles are reversed.) 
> Seems like the class of such functions (if any exist) might
> have some interesting properties...
> 
> DG
> 
> > Don't forget that the only difference between FFT and
> iFFT
> > is (besides
> > of teh scaling factor) a minus sign in the exponent.
> > 
> > Matthieu
> > 
> > 2009/6/9 bela <bela.mihalik@gmail.com>:
> > >
> > > I tried to calculate the second fourier
> transformation
> > of an image with the
> > > following code below:
> > >
> > >
> >
> ---------------------------------------------------------------
> > > import pylab
> > > import numpy
> > >
> > > ### Create a simple image
> > >
> > > fx = numpy.zeros( 128**2
> ).reshape(128,128).astype(
> > numpy.float )
> > >
> > > for i in xrange(8):
> > >        for j in xrange(8):
> > >                fx[i*8+16][j*8+16] = 1.0
> > >
> > > ### Fourier Transformations
> > >
> > > Ffx = numpy.copy( numpy.fft.fft2( fx ).real )  
> # 1st
> > fourier
> > > FFfx = numpy.copy( numpy.fft.fft2( Ffx ).real )
>  #
> > 2nd fourier
> > > IFfx = numpy.copy( numpy.fft.ifft2( Ffx ).real )
>   #
> > inverse fourier
> > >
> > > ### Display result
> > >
> > > pylab.figure( 1, figsize=(8,8), dpi=125 )
> > >
> > > pylab.subplot(221)
> > > pylab.imshow( fx, cmap=pylab.cm.gray )
> > > pylab.colorbar()
> > > pylab.title( "fx" )
> > >
> > > pylab.subplot(222)
> > > pylab.imshow( Ffx, cmap=pylab.cm.gray )
> > > pylab.colorbar()
> > > pylab.title( "Ffx" )
> > >
> > > pylab.subplot(223)
> > > pylab.imshow( FFfx, cmap=pylab.cm.gray )
> > > pylab.colorbar()
> > > pylab.title( "FFfx" )
> > >
> > > pylab.subplot(224)
> > > pylab.imshow( IFfx, cmap=pylab.cm.gray )
> > > pylab.colorbar()
> > > pylab.title( "IFfx" )
> > >
> > > pylab.show()
> > >
> >
> ---------------------------------------------------------------
> > >
> > > On my computer FFfx is the same as IFfx..... but
> why?
> > >
> > > I uploaded a screenshot about my result here:
> > > http://server6.theimagehosting.com/image.php?img=second_fourier.png
> > >
> > > Bela
> > >
> > >
> > > --
> > > View this message in context: http://www.nabble.com/second-2d-fft-gives-the-same-result-as-fft%2Bifft-tp23945026p23945026.html
> > > Sent from the Numpy-discussion mailing list
> archive at
> > Nabble.com.
> > >
> > > _______________________________________________
> > > Numpy-discussion mailing list
> > > Numpy-discussion@scipy.org
> > > http://mail.scipy.org/mailman/listinfo/numpy-discussion
> > >
> > 
> > 
> > 
> > -- 
> > Information System Engineer, Ph.D.
> > Website: http://matthieu-brucher.developpez.com/
> > Blogs: http://matt.eifelle.com and http://blog.developpez.com/?blog=92
> > LinkedIn: http://www.linkedin.com/in/matthieubrucher
> > _______________________________________________
> > Numpy-discussion mailing list
> > Numpy-discussion@scipy.org
> > http://mail.scipy.org/mailman/listinfo/numpy-discussion
> > 
> 
> 
>       
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