dft.m

## dft.m
% it creates a simple gray image (4x4)
I = [255, 255, 30, 100
    255, 50, 90, 20
    70, 70, 20, 10
    100, 20, 10, 0];
% it converts it to grayscale
I = mat2gray(I);
% shows it
imshow(I);

IDFT = [];

% DFT
N1 = 4;
N2 = 4;
e = exp(1);

% DFT implementation
for u=0:(N1-1)
  for v=0:(N2-1)
      % X(u, v)
      DFT = 0;
        for x=0:(N1-1)
            for y=0:(N2-1)
                Intensity = I(x+1,y+1);
                FirstDimension = e ^ (-1i*( (2*pi/N1) * u * x));
                SecondDimension = e ^ (-1i*( (2*pi/N2) * v * y));
                DFT = DFT + (Intensity * FirstDimension * SecondDimension);
            end
        end
       IDFT(u+1, v+1) = DFT;
  end
end


IDFT
%MATLAB_FFT=fft2(I)

surf(log(abs(fftshift(IDFT))));

InverseI=abs(ifft2((IDFT)))
I