Hilbert transform: Applications to atomic spectra

In many areas of physics, the Kramers-Kronig 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 while avoiding the use of complicated experimental setups.