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Re: image 2-d Fouriertransform ?

• To: mathgroup at smc.vnet.net
• Subject: [mg21902] Re: image 2-d Fouriertransform ?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 4 Feb 2000 02:54:36 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <87av1h$nun@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

the result of the 2d Fourier[] call is in the interval kx,ky \in
[0,2Pi].
"Important" are the kx,ky with small absolute values , but with the
periodic
condition in kx and ky. So every quadrant in your image is important
because
a ki near 2Pi will map to a small ki in the periodic repeated area. You
can
use

ShiftMatrix[m_?MatrixQ] := 
  RotateLeft[RotateLeft[#, Length[#]/2] & /@ m, Length[m]/2]

on your Fourier output. This shift the interval from ki \in [0,2Pi] to
ki \in [-Pi,Pi] and all what is close to the center (the origin) of the
image
is important.


Hope that helps
  Jens

maurus wrote:
> 
> 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