fourier transform - Create an aliased image in FD

Is there an accurate way to create an aliased image from the Fourier transform of the original image?

in other words, i have the Fourier coefficients of an image and i want to make down-sample in frequency domain.

Answer

I am trying to construct an aliasing image.

I=rgb2gray(imread('Liver.png')); % a 512*512 image 
subplot(1,2,1),imshow(I),title('Original image')  % shown on the left side of figure below

when you implement F=fftshift(fft2(I));, the corresponding axis represent the frequency range of [-255:256]/512; and the cut-off frequency U = V = 256/512 = 0.5;

based on Nyquist Sampling Theorem, the sampling periods in spatial domain should satisfy

delta_x<=1/(2*U)=1;
delta_y<=1/(2*V)=1;

to avoid the aliasing.

So if your bandwidth of recorder is 64 * 64, the corresponding point interval in spatial domain is 1 / (64/256) = 4. Thus,

Ia=imresize(I(1:4:end,1:4:end),[512 512]);
subplot(1,2,2),imshow(Ia),title('Aliased image') % shown on the right side of the figure below

You can observe the aliasing effect at the edge.