Scaling the fft

Hi

I am trying to perform an fft on some data but have been
having trouble with the scaling of the frequency axis. I
started testing things with gaussians. If one starts with
a gaussian of full width half maximum of 1.386a then the
resulting gaussian on transform is expected to have width
0.44/a. This is a well known mathematical result.

I defined a number of gaussians of various widths and then
took the fft of each. Each gaussian is defined over 32,768
points (2^15) and thus the fft returned equally has 2^15
points. For example define a gaussian with mean 0,
standard deviation 1 over the range x = (-
16.384:0.001:16.383). When plotting the fft values returned
against the original time axis (x) of the input gaussian
one would expect to find that a common scaling factor is
required to scale the x-axis in order to give the gaussians
the correct widths - indeed it is...21.625

When I repeat this using box functions of various widths
however the scaling factor required changes depending on
the box function and is certainly never equal to 21.625 as
before. For a box function of width 'a' one expects that
the fft is a sinc function with first minima at 1/a.

So why does the scaling factor change in different cases?
This should be the same for ANY 32,768 point function.

Many thanks

Ben
.

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