  In many areas of physics, the Kramers-Kronig (KK) relations are used to
extract information about the real part of the optical response of a medium
from its imaginary counterpart. In this paper we discuss an alternative but
mathematically equivalent approach based on the Hilbert transform. We apply the
Hilbert transform to transmission spectra to find the group and refractive
indices of a Cs vapor, and thereby demonstrate how the Hilbert transform allows
indirect measurement of the refractive index, group index and group delay
whilst avoiding the use of complicated experimental set ups.
