The Fourier spectra of the fields from a uniformly moving harmonic source are investigated. These spectra are found as space integrals of a dyadic Green's function multiplied with the source current density. The spectra turn out to be bandlimited and to evidence two (infinite) peaks. The analysis is valid for arbitrary velocities and for arbitrary distances between the source volume and the observation point. The spectra of the fields from a moving dipole are treated in some detail.