  We obtain analytical gravitational waveforms in the frequency-domain for
precessing, quasi-circular compact binaries with small spins, applicable, for
example, to binary neutron star inspirals. We begin by calculating an analytic
solution to the precession equations, obtained by expanding in the
dimensionless spin parameters and using multiple-scale analysis to separate
timescales. We proceed by analytically computing the Fourier transform of
time-domain waveform through the stationary phase approximation. We show that
the latter is valid for systems with small spins. Finally, we show that these
waveforms have a high overlap with numerical waveforms obtained through direct
integration of the precession equations and discrete Fourier transformations.
The resulting, analytic waveform family is ideal for detection and parameter
estimation of gravitational waves emitted by inspiraling binary neutron stars
with ground-based detectors.
