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main.m

+clear;close all; clc;
+%% Question 1
+data = im2double(imread("car_dis.png"));
+[N,M] = size(data);
+figure(Name="Orginal Image");
+imshow(data);
+% Calculate and display the fourier transform
+f_data = fft2(data);
+plot_spectrum(f_data,"Fourier transform","Q1, Fourier transform");
+% Save figure
+print -r150 -dpng Imlogmag.png
+
+%% Question 3
+h = fspecial("average",[1,9]);
+filtered = imfilter(data,h,"replicate","corr");
+figure(Name="Q3, Using fspecial and imfilter")
+imshow(filtered,[])
+print -r150 -dpng Q3_filter_image.png
+% Calculate and display the fourier transform
+f_filtered = fft2(filtered);
+plot_spectrum(f_filtered,"Fourier transform","Q3, Fourier transform");
+% Save figure
+print -r150 -dpng Q3_filter_Fourier.png
+
+%% Question 4
+OTF = psf2otf(h,[N,M]);
+figure(Name="Q4, OTF");
+imshow(fftshift(abs(OTF)),[])
+label_figure("u","v","abs(OTF)",true);
+print -r150 -dpng Q4_abs_OTF.png
+fprintf("Q4.b Attenuation factor: %f\n",OTF(129,157));
+
+%% Question 5
+sx = 25;  % Horizontal size (should be uneven)
+sy = 13;  % Vertical size  (should be uneven)
+row_f = 129; col_f = 157;
+r0 = row_f-(sy-1)/2;   r1 = row_f+(sy-1)/2;
+c0 = col_f-(sx-1)/2;   c1 = col_f+(sx-1)/2;
+H = ones(N,M);
+H([r0:r1 r0:r1],[M-c1+2:M-c0+2 c0:c1]) = 0;
+H = circshift(H,-floor(size(H)/2));
+f_data_filtered = f_data .* H;
+figure(Name="Q5 OTF"); imshow(fftshift(abs(H)),[]); label_figure("u","v","abs(OTF)",true);
+print -r150 -dpng Q5_OTF.png
+% Transform back
+inv = ifft2(f_data_filtered);
+fprintf("Q5 max imag component: %i\n",max(abs(imag(inv(:)))))
+figure(Name=sprintf("Q5, %i, %i",sx,sy)); imshow(inv,[])
+gca.Visible = 'off';
+print -r150 -dpng Q5_filtered_image.png
+plot_spectrum(fft2(inv),"Fourier transform newly filtered image","Q5, Fourier transform");
+print -r150 -dpng Q5_OTF_FFT.png
+%% Functions
+function plot_spectrum(data,title_str,fig_title)
+    figure(Name=fig_title);
+    imagesc(log(fftshift(abs(data))+1));
+    colormap("turbo"); colorbar();
+    label_figure("u","v",title_str,true);
+end
+
+function label_figure(x_label,y_label,title_str,hide_axis)
+    if (hide_axis)
+        ax = gca;
+        ax.XTick = [];
+        ax.YTick = [];
+    end
+    title(title_str);
+    xlabel(x_label);
+    ylabel(y_label);
+end
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