  Almost every galaxy has a supermassive black hole (SMBH) residing at its
center, the Milky Way included. Recent studies suggest that these unique places
are expected to host a high abundance of stellar and compact object binaries.
These binaries form hierarchical triple systems with the SMBH and undergo the
eccentric Kozai-Lidov (EKL) mechanism. Here we estimate the detectability of
potential Gravitational-Wave emissions from these compact objects within the
frequency band of the Laser Interferometer Space Antenna (LISA) and Laser
Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors. We
generate a post EKL population of stars at the onset of Roche limit crossing
and follow their evolution to compact object binaries. As a proof-of-concept,
we adopt two metallicities, solar metallicity ($Z = 0.02$) and $15\%$ of it ($Z
= 0.003$). We demonstrate that over the observation timescale of LISA, black
hole binaries (BH-BH) and white dwarf binaries provide the most prominent GW
sources via the EKL assisted merger channel. Systems involving neutron stars
are less observable but possibly abundant through different merger channels.
Our population synthesis of BH-BH with $Z = 0.02$ ($Z = 0.003$) translate to
$\sim$ $4$ ($24$) events per year with LIGO within a 1 ${\rm Gpc}^3$ sphere. We
also estimated the number of binaries visible in the LISA band within the inner
parsec of our galactic center (and possibly other galaxies) to be about 14 -
150 WD-WD, 0 - 2 NS-BH, 0.2 - 4 NS-NS, and 0.3 - 20 BH-BH.
