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We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by"stitching" together a long inspiral waveform from a sequence of waveformsnapshots, each of which corresponds to a particular geodesic orbit. We showthat the complicated total waveform can be regarded as a sum of "voices." Eachvoice evolves in a simple way on long timescales, a property which can beexploited to efficiently produce waveform models that faithfully encode theproperties of EMRI systems. We look at examples for a range of differentorbital geometries: spherical orbits, equatorial eccentric orbits, and oneexample of generic (inclined and eccentric) orbits. To our knowledge, this isthe first calculation of a generic EMRI waveform that uses strong-fieldradiation reaction. We examine waveforms in both the time and frequencydomains. Although EMRIs evolve slowly enough that the stationary phaseapproximation (SPA) to the Fourier transform is valid, the SPA calculation mustbe done to higher order for some voices, since their instantaneous frequencycan change from chirping forward ($\dot f > 0$) to chirping backward ($\dot f <0$). The approach we develop can eventually be extended to more complete EMRIwaveform models, for example to include effects neglected by the adiabaticapproximation such as the conservative self force and spin-curvature coupling.

Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency