# Average intensity as a function of angle in 2D FFT plot

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Prabhat Srivastava on 15 Feb 2021
Hi
I have a 2D FFT spectrum plot of an image which looks like as shown in the image. I want to get the average value of amplitudes as a function of angle(0 to 360) around the center.
How do i go about it? I tried to convert it into polar coordinate but I am not sure how is it being converted!

Bjorn Gustavsson on 15 Feb 2021
This is kind-of-difficult in practice. Your fft has low-wavenumber components at [0,0], [1,0], [-1, 0], [0,1], [0,-1] and if we include the components with norm 2^(1/2) at [1,1], [-1,1], [-1,-1] and [1,-1]. The non-DC components are at 0, 90, 180 and 270 degrees angle, and then 45, 135, 225, and 315 degrees. It is not at all clear to me that you can trivially interpolate between these Fourier-components. What I suggest is that you rotate your image with imrotate, and then do the fft and extract the horizontal and vertical components from those ffts to get the angular variation. By doing that it is at least clear what interpolation-effects are introduced.
HTH
Prabhat Srivastava on 17 Feb 2021
HI Bjourn
Thank you for the help. But I didn't do it in matlab. I did it in imageJ, and just took the average intensity at some required angle.
Thank you once again.