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## Re: Help-octave Digest, Vol 126, Issue 4

 From: Yaowang Li Subject: Re: Help-octave Digest, Vol 126, Issue 4 Date: Tue, 6 Sep 2016 10:37:24 -0400

Dear Dave,

Thank you very much for your response.

I understand the Octave index starting from 1, not 0. and I did not find the what I want. That is why I ask this question.

On the purpose of making it clearer. I enclosed my script and the example image. Hope to help you to find where is wrong.

Best Regards,

Yaowang

On Tue, Sep 6, 2016 at 9:39 AM, Dave Cottingham wrote:
Yaowang writes:

For a real function, for example, an image (u), Its Fourier transform
should follow the Friedel symmetry, I mean the U(s) = U*(-s). Here,
U(s) is the Fourier transform of u, and is a complex number. U*(s) is
its conjugate. I tested two images in imagej, and it works. However, it
is not happen in Octave, the real part is not equal and the imaginary
part is not opposite. They should have the magnitude and opposite
phase. That is what is my question. that is what I did in Octave.

%Fourier transform
img1_sf=fft2(double(img1));
img2_sf=fft2(double(img2));

Thank you very much.

Best Regards,

Yaowang

The element for s = (0, 0) is stored at index (1, 1), and the indexing is modulo the size of the array.

For example, suppose your image is of size 64 x 64. Then s = (1, 2) is at index (2, 3), and s = (-1, -2) is at index (64, 63). If you use this indexing rule, you should see the complex conjugate relation you expect.

- Dave Cottingham friedel_symmetry.m
Description: Text Data fibers01.tif
Description: TIFF image