gauss_lowpass.m

x=imread('Fig4.11(a).jpg');
subplot(211);imshow(x,[]);title('Original Image');
dimension=size(x);
D0=15;
x=double(x);

M=dimension(1);
N=dimension(2);

filt=zeros(M,N);         % filter

for i=1:M
    for j=1:N
%         if((abs(i-M/2)<D0)&(abs(j-N/2)<D0))
%         if((sqrt(((i-M/2)^2)+((j-N/2)^2)))<D0)
             filt(i,j)=exp(-((i-M/2).^2+(j-N/2).^2)/(2*(D0^2)));;
%               filt(i,j)=1;
        end
    end
end
freq_im=fft2(x);

freq_im=fftshift(freq_im);


y=(1/(M*N))*freq_im;   % 1/MN should be added by the user

% figure
% imshow(y)

filt_im=y.*filt;
new_freq=ifftshift(filt_im);
new_im=ifft2(new_freq,M,N);

% imshow(filt,[])
%  imshow(filt_im);
% 

subplot(212);imshow(new_im,[]);title('Low Pass Image');