  Gravitational waves emitted by inner binaries in hierarchical triple systems
are interesting astrophysical candidates for space-based detectors like the
Laser Interferometer Space Antenna, LISA. In the presence of a third body, such
as a supermassive black hole, an inner binary consisting of intermediate mass
black holes can undergo oscillations in eccentricity and inclination angle due
to the Kozai-Lidov mechanism. In this work, we construct analytic gravitational
waveforms in the Fourier domain, taking into account the Kozai-Lidov effect at
Newtonian (leading) order. Using multiple-scale analysis, we make use of the
separability of timescales to combine the effects of both Kozai-Lidov
oscillations and radiation-reaction. We assume small eccentricity and present
analytic solutions to the evolution of the other orbital elements. Our analytic
calculation can be systematically extended to higher orders in eccentricity,
and can be used to construct inspiral-merger-ringdown models. The imprint on
the waveform, due to this combined evolution, is computed under the
stationary-phase approximation. We find that the oscillations leave a clear
signature on the Fourier amplitude of the waveform while leaving a measurable
imprint on the gravitational wave phase, and that our analytic results are
consistent with numerics. Further, with our study of the astrophysical
parameters of the hierarchical triple, we outline potential source candidates,
along with potential implications for gravitational wave data analysis.
