Multidimensional discrete Fourier transforms

*To*: mathgroup at smc.vnet.net*Subject*: [mg104098] Multidimensional discrete Fourier transforms*From*: markus <markusg.phys at googlemail.com>*Date*: Mon, 19 Oct 2009 07:11:39 -0400 (EDT)

Hello, 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 diagonal)? Maybe this question is trivial, but I find the issue of multidim. FTs not so well described in the Mathematica documentation... Thanks, Markus