  We provide ready-to-use time-domain gravitational waveforms for spinning
compact binaries with precession effects through 1.5PN order in amplitude and
compute their mode decomposition using spin-weighted -2 spherical harmonics. In
the presence of precession, the gravitational-wave modes (l,m) contain
harmonics originating from combinations of the orbital frequency and precession
frequencies. We find that the gravitational radiation from binary systems with
large mass asymmetry and large inclination angle can be distributed among
several modes. For example, during the last stages of inspiral, for some
maximally spinning configurations, the amplitude of the (2,0) and (2,1) modes
can be comparable to the amplitude of the (2,2) mode. If the mass ratio is not
too extreme, the l=3 and l=4 modes are generally one or two orders of magnitude
smaller than the l = 2 modes. Restricting ourselves to spinning, non-precessing
compact binaries, we apply the stationary-phase approximation and derive the
frequency-domain gravitational waveforms including spin-orbit and spin(1)-
spin(2) effects through 1.5PN and 2PN order respectively in amplitude, and
2.5PN order in phase. Since spin effects in the amplitude through 2PN order
affect only the first and second harmonics of the orbital phase, they do not
extend the mass reach of gravitational-wave detectors. However, they can
interfere with other harmonics and lower or raise the signal-to-noise ratio
depending on the spin orientation. These ready-to-use waveforms could be
employed in the data-analysis of the spinning, inspiraling binaries as well as
in comparison studies at the interface between analytical and numerical
relativity.
