  The energy radiated (without the 1.5PN tail contribution which requires a
different treatment) by a binary system of compact objects moving in a
hyperboliclike orbit is computed in the frequency domain through the second
post-Newtonian level as an expansion in the large-eccentricity parameter up to
next-to-next-to-leading order, completing the time domain corresponding
information (fully known in closed form at the second post-Newtonian of
accuracy). The spectrum contains quadratic products of the modified Bessel
functions of the first kind (Bessel K functions) with frequency-dependent order
(and argument) already at Newtonian level, so preventing the direct evaluation
of Fourier integrals. However, as the order of the Bessel functions tends to
zero for large eccentricities, a large-eccentricity expansion of the spectrum
allows for analytical computation beyond the lowest order.
