1. M/2 M
N/2 N

2. DFT of images a=[zeros(256,128) ones(256, 128)]; af=fftshift(fft2(a));
imshow(log(1+abs(af)), []); % apply log transform to increase contrast

3. DFT of images (cont.)
Exercise#1: show the magnitude of DFT of the following images
a=zeros(256, 256);
a(78:178, 78:178)=1;
[x,y]=meshgrid(-128:127, -128:127);
z=sqrt(x.^2+y.^2);
c=(z<15);
cameraman.tif

4. Filtering : ideal low pass filter
cm=imread('cameraman.tif');
cm=double(cm);
cf=fftshift(fft2(cm));
figure, imshow(log(abs(cf)+1), [])
cf1=cf.*c;
figure, imshow(log(abs(cf1)+1), [])
cf1i=ifft2(cf1);
figure, imshow(abs(cf1i), [])
Ex#2 Perform ideal low pass filtering with
cut-off frequency D=5 and D=30
Ex#3 Perform ideal high pass filtering with
cut-off frequency D=5 and D=30

5. Filtering: Butterworth filter
[x,y]=meshgrid(-128:127, -128:127);
b1=1./(1+((x.^2+y.^2).^0.5/15).^4);
Ex#4 Perform Butterworth low-pass and high-pass filtering
with cut-off frequency D=15 and n=2 to cameraman