The controlled and accurate emission of coherent electronic wave packets is of prime importance for future applications of nanoscale electronics. Here, we present a theoretical and experimental analysis of the finite-frequency noise spectrum of a periodically driven single-electron emitter. The electron source consists of a mesoscopic capacitor that emits single electrons and holes into a chiral edge state of a quantum Hall sample. We compare experimental results with two complementary theoretical descriptions: on the one hand, the Floquet scattering theory that leads to accurate numerical results for the noise spectrum under all relevant operating conditions, and on the other hand, a semiclassical model that enables us to develop an analytic description of the main sources of noise when the emitter is operated under optimal conditions. We find excellent agreement between experiment and theory. Importantly, the noise spectrum provides us with an accurate description and characterization of the mesoscopic capacitor when operated as a periodic single-electron emitter.