  The detection of GW150914 by ground based gravitational wave observatories
has brought about a new era in astrophysics. At optimal sensitivity, these
observatories are expected to detect several events each year, with one or two
of these occurring with non-negligible eccentricity. Such eccentric binaries
will emit bursts of gravitational radiation during every pericenter passage,
where orbital velocities can reach greater than ten percent the speed of light.
As a result, such binaries may prove to be powerful probes of extreme
gravitational physics and astrophysics. A promising method of achieving
detection of such binaries is through power stacking, where the power in each
burst is added up in time-frequency space. This detection strategy requires a
theoretical prior of where the bursts will occur in time and frequency so that
one knows where to search for successive bursts. We here present a generic
post-Newtonian formalism for constructing such time-frequency model priors at
generic post-Newtonian order. We apply our formalism to generate a burst model
at third post-Newtonian order, making it potentially the most accurate, fully
analytic model to date.
