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OT: on the DFT of a periodic Gaussian kernel (analytic representation?)

Globe Trotter 
Hi,

I have a one-dimensional N-coordinate periodic Gaussian kernel defined by 

dnorm(c(0:N/2,(N/2-1):1),sd = h)

where h is the bandwidth/smoothing parameter/FWHM.

I want to calculate the Fourier transform of this, which can be done using a
FFT. But my question is: is it possible to get the Discrete Fourier transform
of this sequence analytically? Do there exist references on this?

Many thanks and best wishes,
Aarem