How to perform 2D Inverse Discrete Fourier Transformation for the given specific problem?

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I have this problem where i need to numerically evaluate the 2D inverse Fourier transform of the below given problem at .
We know the values of the given Fourier transformed function inside the integral as a square matrix by [N x N].
First question: Is it possible to define function such that;
If we can do it, then can we evaluate numerically?

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