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Math Help - Effect of phase shifting the Fourier transform

  1. #1
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    Effect of phase shifting the Fourier transform

    Hello!

    I am trying to do the following experiment using MATLAB (this is a math question, not a MATLAB question):

    1) Calculate the 2D Fourier transform of a grayscale image (range: 0-1/black=0,white=1)
    2) Phase shift every single (complex!) pixel in the 2D Fourier transform with the same phase shift value (e.g. 0.5 becomes 0.5i with a phase shift of pi/2)
    3) Do an inverse 2D Fourier transform (after the phase shifting) and obtain a new image.

    The code I used for the phase shifting:
    absoluteValue = abs(fourierImage);
    phase = angle(fourierImage) + phaseShift_rad;
    newFourierImage = absoluteValue .* exp(phase * 1i);

    The thing is that after doing this, the new image looks exactly the same as the original image, however the pixels in the new image are plotted as the absolute value of that pixel. Plotting only the real part does yield a different result, but these are really distorted images, so I am just plotting the absolute values.

    My question is: is it correct that the absolute value of the new image looks exactly the same as the original image? If not, what should I be expecting to see?

    Thanks for your time
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  2. #2
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    Re: Effect of phase shifting the Fourier transform

    greyscale pixels are one dimensional objects. They have amplitude and that's all. Applying a phase shift to a greyscale image will have no effect as a phase shift doesn't affect the amplitude.

    Phase shifts will very much have effect if you start performing complex filtering on the image or do coherent combination of images, but won't affect just the appearance of the image.
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  3. #3
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    Re: Effect of phase shifting the Fourier transform

    I am not phase shifting the image itself, but its Fourier transform (which does have complex pixels). Even when I give each line of complex pixels in the Fourier transform a different phase shift, the new image (after the inverse 2D Fourier transform) still looks the same. Is this correct? Why does this happen? Some mathematical insight would be nice
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  4. #4
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    Re: Effect of phase shifting the Fourier transform

    Anyone?
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