How can I implement a 2D DFT?

I have been trying to implement a 2D DFT but the code is not working properly and I cannot find the bug. Can anyone help me?

im = zeros(8,8);
im(1,1) = 1;
[r_im, c_im] = size(im);

S_2 = zeros (size(im));
values = zeros(size(im));

for ky = 1:8
    for kx = 1:8
        for  y = -3:4 
            for  x = -3:4
               values(y+4,x+4) = im(y+4,x+4)*exp(((-2i)*pi)*((kx*x/c_im)+(ky*y/r_im)));
            end
        end       
        S_2(ky,kx) = sum(sum(values));
        values(:,:) = 0;        
    end
end
S_2 = fftshift(S_2);
MRI_im_2 = abs(ifft(S_2));

figure,
subplot(1,3,1),imshow(im), title('Original Image'); 
subplot(1,3,2),imshow(S_2,[]),title('FFT Simulation'); 
subplot(1,3,3),imshow(MRI_im_2,[]), title('IFFT Simulation');

[Image Analyst]

It runs without error. What do you think it's not working? Supply more information about what you think is not right. It's just doing what you told it to.

[SA]

@Image Analyst, I've also experienced problems implementing 2d DFT for spatial spectrum. Can you please help me regarding that link https://www.mathworks.com/matlabcentral/answers/1609940-problems-to-plot-2d-wave-vector-versus-spatial-spectrum-obtained-from-cross-spectral-densities-of-se

Answer 1

[Kushagr Gupta]

It might also help to compare the result of code written with the inbuilt MATLAB 2D FFT function 'fft2'.

Documentation for the 'fft2' function is available at the following link:

https://www.mathworks.com/help/matlab/ref/fft2.html

Answer 2

[Image Analyst]

Attached are my 2D fft demos.