If your problem is the A
in the exponent you just have to do a variable transformation.
Then the integral you have to calculate is
matrix(u,v) = A^-2 integral integral matrix(x,y) exp(-i(ux+vy))dx dy
Doing this, you then can just use fft2
:
M_uv = A^-2 * fft2(M_xy)
where M_xy
is your matrix(x,y) and M_uv
then would be the resulting Fourier transform matrix(u,v).