Re: [Numpy-discussion] second 2d fft gives the same result as fft+ifft
I made the transformations with scipy. It works with complex numbers. The results are here: http://server6.theimagehosting.com/image.php?img=second_fourier_scipy.png Also i asked it from others... as i understand now: the second fourier transformation of a function always gives back the mirror of the function itself. I didn't know it :-) thanks, bela 2009/6/9 David Goldsmith d_l_goldsm...@yahoo.com 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_goldsm...@yahoo.com wrote: From: David Goldsmith d_l_goldsm...@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.bruc...@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.miha...@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 ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
[Numpy-discussion] second 2d fft gives the same result as fft+ifft
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
Re: [Numpy-discussion] second 2d fft gives the same result as fft+ifft
Hi, Is it really ? You only show the imaginary part of the FFT, so you can't be sure of what you are saying. 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.miha...@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
Re: [Numpy-discussion] second 2d fft gives the same result as fft+ifft
--- On Tue, 6/9/09, Matthieu Brucher matthieu.bruc...@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.miha...@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 ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] second 2d fft gives the same result as fft+ifft
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_goldsm...@yahoo.com wrote: From: David Goldsmith d_l_goldsm...@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.bruc...@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.miha...@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 ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
