  The purpose of this paper is to investigate the radiation process of the
charged particle passing through an external periodic field in a dispersive
medium. In the optical range of spectrum we will consider two cases: first, the
source has not eigenfrequency, and second, the source has eigenfrequency. In
the first case, when the Cherenkov radiation occurs, the non-zero
eigenfrequency produces a paradox for Doppler effect. It is shown that the
absence of the eigenfrequency solves the paradox known in the literature. The
question whether the process is normal (i.e. hard photons are being radiated
under the small angles) or anomalous depends on the law of the medium
dispersion. When the source has an eigenfrequency the Doppler effects can be
either normal or anomalous. In the X-ray range of the oscillator radiation
spectrum we have two photons radiated under the same angle- soft and hard. In
this case the radiation obeys to so-called complicated Doppler effect, i.e. in
the soft photon region we have anomalous Doppler effect and in the hard photon
region we have normal Doppler effect.
