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Multidimensional discrete Fourier transforms


I have the following question related to the "Fourier" function:
Assume I have a 2D list v={{..,..},...} of values and I want to plot
the Fourier spectrum for multiples of a certain wave vector k:=
{kx,ky}, say k=p*{1,1} for simplicity.
Mathematically, the Fourier transform of my list would be something
like vFT(kx,ky) = \sum_(x,y) \exp(i (kx,ky) * (x,y)) v(x,y), where *
is the scalar product.

Now, my question is, whether the output of Fourier[v] is just an array
with indices corresponding to kx and ky (and hence the values
corresponding to the wavevectors p*{1,1} would be just on the
Maybe this question is trivial, but I find the issue of multidim. FTs
not so well described in the Mathematica documentation...


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