clear;
nx = 200;
ny = 600;
for i = 1:nx   % Define the big wave with periodic noise.
  for j = 1:ny
      u(i,j) = 0+100*(1+sin(2*pi*((j-1)/ny)*5)) + ...
                    15.*(1+sin(2*pi*((i-1)/nx)*80))+...
                    15.*(1+sin(2*pi*((j-1)/ny)*80));
  end
end
sine = uint8(u);
imwrite(sine, 'sine.jpg');
fftu = fft2(u,2*nx-1,2*ny-1);   % Padded fft.
fftu = fftshift(fftu);
figure(1);
mesh(u');
figure(2)
mesh(log(1+(abs(fftu))));
filter = ones(2*nx-1,2*ny-1);
d0 = 150;                     % Use ideal low pass filter.
for i = 1:2*nx-1
    for j =1:2*ny-1
        dist = ((i-(nx+1))^2 + (j-(ny+1))^2)^.5;
        if dist > d0
            filter(i,j) = 0;
        end
    end
end 
figure(3)
mesh(filter);
fil_sine  = filter.*fftu;
figure(4)
mesh(log(1+abs(fil_sine)));
fil_sine = ifftshift(fil_sine);
fil_sine = ifft2(fil_sine);  
fil_sine = real(fil_sine(1:nx,1:ny));
fil_sine = uint8(fil_sine);
imwrite(fil_sine, 'sine_fil.jpg');