Re: image 2-d Fouriertransform ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg21922] Re: image 2-d Fouriertransform ?*From*: "Mariusz Jankowski" <mjkcc at usm.maine.edu>*Date*: Fri, 4 Feb 2000 02:54:49 -0500 (EST)*Organization*: University of Southern Maine*References*: <87av1h$nun@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Maurus, a real signal cannot be uniquely represented by 1 quarter of the 2D discrete Fourier transform (DFT) coefficients. I will use the following non-symmetric 4 by 4 array: img={{1,2,1,0},{1,1,0,0},{0,0,0,0},{0,0,0,0}}; MatrixForm[Partition[InverseFourier[img],{2,2}]] (* I use InverseFourier as my definition of the DFT, as is common in engineering, signal processing *) The coefficients have complex conjugate symmetry - they are all related, not random. For a short explanation on the ordering of the coefficients in 1D (think of a single row or column of your 2D transform) see MathGroup archives from approx 2 weeks ago. Also take a look at my notebooks on Fourier series and transform in Wolfram's courseware catalog http://library.wolfram.com/courseware/. I will be adding a comprehensive set of notebooks on digital image processing to the courseware catalog in the next couple of month - they may be helpful, if you can wait that long. Hope this helps, Mariusz ====================================================== Mariusz Jankowski University of Southern Maine mjkcc at usm.maine.edu "maurus" <maurus at gmx.de> wrote in message news:87av1h$nun at smc.vnet.net... > Hello, > > sorry for this question but .. > > i have a 2-d image with 8 bit grey level. > Now i make a 2-d-Fouriertransform of the image (in Mathematica) > The result is a Picture with 4 quadrants, were the signals are > significant. > > Now my questions: > I think, only the first quadrant ist important ? Rest ist random ? > What does the axis, the results means ? > > > > If someone canl help me, i can send an example for better understanding. > > In this case, the Helpfunktion in Mathematica ist not to good. > > Thanks in advance > > Maurus > >