I am trying to match the excel FT (Fourier Transform) of a Gaussian to the analytical FT.
My Column A goes from 0 to 4095, column B goes from -2048 to 2047.
Column C is: C1=(1/200sqrt(2 pi())) exp(-0.5(B1/200)^2), which is a Gaussian.
Using Excel's Fourier Analysis pack, I FT column C and put the output in Column G.
Column H is: H1=IMABS(G1).
Column F is: F1=A1/4096.
Column J is the analytical FT of the Gaussian: J1=exp(-0.5*(F1*200)^2).
But, columns H and J do not match (using column F as the x-axis). Oddly enough, columns H and J match up great when I change column F to F1=A1/650. But why 650? It makes no sense. The same is true when I change the SD from 200 to 100.
Since your original interval has length 4096, the fundamental frequency (with one full wave fitting on that interval) is $f_1=2\pi/4096$. The frequencies for which the result is computed by a discrete Fourier transform are multiples of this $f_1$.
So you should have computed your analytical control result for those same frequencies, which means that column F should have been filled with $2\pi/4096$ times column A. Now $2\pi/4096$ happens to be $1/ 651.8986...$, so that is essentially what you already found.