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How can I get the FFT matrix?

I have an image with index data [-(N-1)/2, .., 0,...,(N-1)/2] x [-(N-1)/2, .., 0, ..., (N-1)/2] and I need for a special calculation only the DFT, rather the FFT, matrix F, such that X = Fx, where X is the frequency sequence and x the real domain sequence.

Is there any routine that I can use that calculates the FFT matrix??