  In this work we analyze the gravitational wave signal from hypermassive
neutron stars formed after the merger of binary neutron star systems, focusing
on its spectral features. The gravitational wave signals are extracted from
numerical relativity simulations of models already considered by De Pietri et
al. [Phys. Rev. D 93, 064047 (2016)], Maione et al. [Classical Quantum Gravity
33, 175009 (2016)], and Feo et al. [Classical Quantum Gravity 34, 034001
(2017)], and allow us to study the effect of the total baryonic mass of such
systems (from $2.4 M_{\odot}$ to $3 M_{\odot}$), the mass ratio (up to $q =
0.77$), and the neutron star equation of state, both in equal and highly
unequal mass binaries. We use the peaks we find in the gravitational spectrum
as an independent test of already published hypotheses of their physical origin
and empirical relations linking them with the characteristics of the merging
neutron stars. In particular, we highlight the effects of the mass ratio, which
in the past was often neglected. We also analyze the temporal evolution of the
emission frequencies. Finally, we introduce a modern variant of Prony's method
to analyze the gravitational wave postmerger emission as a sum of complex
exponentials, trying to overcome some drawbacks of both Fourier spectra and
least-squares fitting. Overall, the spectral properties of the postmerger
signal observed in our simulation are in agreement with those proposed by other
groups. More specifically, we find that the analysis of Bauswein and
Stergioulas [Phys. Rev. D 91, 124056 (2015)] is particularly effective for
binaries with very low masses or with a small mass ratio and that the
mechanical toy model of Takami et al. [Phys. Rev. D 91, 064001 (2015)] provides
a comprehensive and accurate description of the early stages of the postmerger.
