The existence of an inverse Doppler effect in free space is again scrutinized, following some papers predicting the existence of such phenomena in the near zone of a moving oscillating three-dimensional dipole. In the present paper the wave scattered from a perfectly conducting thin cylinder moving in the presence of a plane electromagnetic wave is analyzed. The response of such a cylinder may be considered as due to either a two-dimensional monopole or a two-dimensional dipole in accordance with the polarization of the incident wave. An intensive numerical spectral estimation based on the fundamental definitions of the terms “frequency,” “spectrum,” and “uncertainty” is performed on the scattered wave at various ranges. An inverse Doppler effect was not found for the two-dimensional case. The same analysis was applied to the case of a moving three-dimensional radiating dipole, reconfirming previous results which showed the presence of an inverse Doppler effect in the near zone of the three-dimensional dipole.