  Observations of gravitational-wave signals from binary neutron-star mergers,
like GW170817, can be used to constrain the neutron-star equation of state
(EoS). One method involves modeling the EoS and measuring the model parameters
through Bayesian inference. A previous study has demonstrated the effectiveness
of using a phenomenologically parameterized piecewise polytrope to extract
constraining information from a simulated population of binary neutron-star
mergers. Despite its advantages compared to more traditional methods of
measuring the tidal deformability of neutron stars, notable deficiencies arise
when using this EoS model. In this work, we describe in detail the
implementation of a model built from a spectral decomposition of the adiabatic
index that was used by the LIGO-Virgo Collaboration in to constrain the neutron
star EoS from GW170817. We demonstrate its overall consistency in recovering
the neutron star EoS from a simulated signal to the piecewise polytropic
implementation used in and explain any differences that arise. We find that
both models recover consistent tidal information from the simulate signals with
tightest constraints on the EoS around twice nuclear saturation density. As
expected, the statistical error that arises in the piecewise polytropic
representation near the fixed joining densities is greatly reduced by using the
spectral model. In addition, we find that our choice of prior can have a
dominant effect on EoS constraints
