  We present a new analytic model describing gravitational wave emission in the
post-merger phase of binary neutron star mergers. The model is described by a
number of physical parameters that are related to various oscillation modes,
quasi-linear combination tones or non-linear features that appear in the
post-merger phase. The time evolution of the main post-merger frequency peak is
taken into account and it is described by a two-segment linear expression. The
effectiveness of the model, in terms of the fitting factor or, equivalently,
the reduction in the detection rate, is evaluated along a sequence of
equal-mass simulations of varying mass. We find that all parameters of the
analytic model correlate with the total binary mass of the system. For high
masses, we identify new spectral features originating from the non-linear
coupling between the quasi-radial oscillation and the antipodal tidal
deformation, the inclusion of which significantly improves the fitting factors
achieved by the model. We can thus model the post-merger gravitational-wave
emission with an analytic model that achieves high fitting factors for a wide
range of total binary masses. Our model can be used for the detection and
parameter estimation of the post-merger phase in upcoming searches with
upgraded second-generation detectors, such as aLIGO+ and aVirgo+, with future,
third-generation detectors (Einstein Telescope and Cosmic Explorer) or with
dedicated, high-frequency detectors.
