%% Question 1
figure;
IM = fft2(double_image);
imshow(log(fftshift(abs(IM))+1e+2),[]);
title('Log-amplitude spectrum');
xlabel('u');
ylabel('v');
print('Imlogmag_Ex1_Q1', '-dpng', '-r150'); %%Save image.

%% Question 3
psf = fspecial('average', [7,1]); %% create filter for this image
filtered_image = imfilter(double_image, psf, 'replicate'); %% filter image with the PSF
figure, imshow(filtered_image); %% create dialog showing the filtered image
imwrite(filtered_image,'IMfil.jpg'); %% Save filtedred image

figure;
IM2 = fft2(filtered_image); %% Create fourier transform out of the filtered image
imshow(log(fftshift(abs(IM2))+1e+2),[]); %% Create log-aplitude spectrum with filtered image and show

%% Question 4
figure
otf = psf2otf(psf, size(filtered_image));
imshow(fftshift(abs(otf)),[]);
print('OTF_logmag_Ex4_Q1', '-dpng', '-r150'); %%Save image.