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(fftw.info)What FFTWND Really Computes

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What FFTWND Really Computes
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   The conventions that we follow for the multi-dimensional transform
are analogous to those for the one-dimensional transform. In
particular, the forward transform has a negative sign in the exponent
and neither the forward nor the backward transforms will perform any
normalization.  Computing the backward transform of the forward
transform will multiply the array by the product of its dimensions.
The output is in-order, and the zeroth element of the output is the
amplitude of the zero frequency component.

   The TeX version of this manual contains the exact definition of the
n-dimensional transform FFTW uses.  It is not possible to display the
definition on a ASCII terminal properly.