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We provide ready-to-use time-domain gravitational waveforms for spinningcompact binaries with precession effects through 1.5PN order in amplitude andcompute their mode decomposition using spin-weighted -2 spherical harmonics. Inthe presence of precession, the gravitational-wave modes (l,m) containharmonics originating from combinations of the orbital frequency and precessionfrequencies. We find that the gravitational radiation from binary systems withlarge mass asymmetry and large inclination angle can be distributed amongseveral modes. For example, during the last stages of inspiral, for somemaximally spinning configurations, the amplitude of the (2,0) and (2,1) modescan be comparable to the amplitude of the (2,2) mode. If the mass ratio is nottoo extreme, the l=3 and l=4 modes are generally one or two orders of magnitudesmaller than the l = 2 modes. Restricting ourselves to spinning, non-precessingcompact binaries, we apply the stationary-phase approximation and derive thefrequency-domain gravitational waveforms including spin-orbit and spin(1)-spin(2) effects through 1.5PN and 2PN order respectively in amplitude, and2.5PN order in phase. Since spin effects in the amplitude through 2PN orderaffect only the first and second harmonics of the orbital phase, they do notextend the mass reach of gravitational-wave detectors. However, they caninterfere with other harmonics and lower or raise the signal-to-noise ratiodepending on the spin orientation. These ready-to-use waveforms could beemployed in the data-analysis of the spinning, inspiraling binaries as well asin comparison studies at the interface between analytical and numericalrelativity.

Higher-order spin effects in the amplitude and phase of gravitational  waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational  waveforms