calculate and show the fourier spectrum for figure 1 (shifted). calculate the average value of the image using the fourier spectrum. in matlab

To calculate and show the Fourier spectrum of an image in MATLAB:

main.m
img = imread('figure1_shifted.jpg');
F = fft2(img);
F_shifted = fftshift(F);
F_spectrum = abs(F_shifted); % absolute value
F_spectrum = log(F_spectrum + 1); % log transform
imshow(F_spectrum, []);
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To calculate the average value of the image using the Fourier spectrum, you can simply calculate the mean value of the Fourier transform:

main.m
avg_value = mean(F_spectrum(:));
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Note that the Fourier spectrum is a complex number, so the absolute value is used to get the amplitude. Also, the log transform is often used to better visualize the spectrum.