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We calculate analytical gravitational waveforms in the time- andfrequency-domain for precessing quasi-circular binaries with spins of arbitrarymagnitude, but nearly aligned with the orbital angular momentum. We firstderive an analytical solution to the precession equations by expanding in themisalignment angle and using multiple scale analysis to separate timescales. Wethen use uniform asymptotic expansions to analytically Fourier transform thetime-domain waveform, thus extending the stationary-phase approximation, whichfails when precession is present. The resulting frequency-domain waveformfamily has a high overlap with numerical waveforms obtained by directintegration of the post-Newtonian equations of motion and discrete Fouriertransformations. Such a waveform family lays the foundations for the accurateinclusion of spin precession effects in analytical gravitational waveforms, andthus, it can aid in the detection and parameter estimation of gravitationalwave signals from the inspiral phase of precessing binary systems.

Gravitational Waveforms for Precessing, Quasi-circular Binaries via Multiple Scale Analysis and Uniform Asymptotics: The Near Spin Alignment Case