  The memory effect in gravitational wave (GW) signals is the phenomenon,
wherein the relative position of two inertial GW detectors undergoes a
permanent displacement owing to the passage of GWs through them. Measurement of
the memory signal is an important target for future observations as it
establishes a connection between observations with field-theoretic results like
the soft-graviton theorems. Theoretically, the memory signal is predicted at
the leading order quadrupole formula for sources like binaries in hyperbolic
orbits. This can be in the realm of observations by Advanced LIGO,
Einstein-Telescope, or LISA for black-holes with masses $\sim$ $O(10^3 \,
M_\odot$) scattered by the super-massive black-hole at the galactic center.
Apart from the direct memory component there is a non-linear memory signal in
the secondary GW emitted from the primary GW chirp-signals emitted by
coalescing binaries. In this paper, we compute the gravitational wave signals
and their energy spectrum using the field-theoretic method by computing the
scattering amplitudes for eccentric elliptical and hyperbolic binary orbits.
The field theoretic calculation gives us the gravitational waveforms of linear
and non-linear memory signals directly in the frequency space. The frequency
domain templates are useful for extracting signals from the data. We compare
our results with other calculations of linear and non-linear memory signals in
literature and point out novel features we find in our calculations like the
presence of $\log(\omega)$ terms in the linear memory from hyperbolic orbits.
