  Recently, we developed effective fly-by (EFB) waveforms designed to model the
burst of gravitational radiation from highly eccentric binaries. We here
present a faster to evaluate frequency domain EFB waveform. The waveform is
constructed through the use of asymptotic expansions of hypergeometric
functions. Since the waveform is fully analytic, we study the accuracy to which
the binary's parameters can be measured using a Fisher analysis. We find that
degeneracies exist among the parameters, such that the waveform is
parameterized in terms of the chirp mass ${\cal{M}}$ and orbital radius of
curvature ${\cal{P}}$, instead of the total mass, symmetric mass ratio, and
semi-latus rectum of the binary. By computing the Fisher matrix for single
bursts from two thousand binary systems, we find that most of the systems will
have greater than one hundred percent uncertainty in the chirp mass, luminosity
distance, and inclination angle, while roughly half will have less than one
hundred percent uncertainty in the orbital radius of curvature, orbital
eccentricity, and polarization angle. Further, we repeat this analysis after
including additional bursts within the inspiral sequence and find that the
uncertainties in the waveform's parameters can improve by orders of magnitude
with a sufficient timing model for the bursts.
