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The purpose of this paper is to investigate the radiation process of thecharged particle passing through an external periodic field in a dispersivemedium. In the optical range of spectrum we will consider two cases: first, thesource has not eigenfrequency, and second, the source has eigenfrequency. Inthe first case, when the Cherenkov radiation occurs, the non-zeroeigenfrequency produces a paradox for Doppler effect. It is shown that theabsence of the eigenfrequency solves the paradox known in the literature. Thequestion whether the process is normal (i.e. hard photons are being radiatedunder the small angles) or anomalous depends on the law of the mediumdispersion. When the source has an eigenfrequency the Doppler effects can beeither normal or anomalous. In the X-ray range of the oscillator radiationspectrum we have two photons radiated under the same angle- soft and hard. Inthis case the radiation obeys to so-called complicated Doppler effect, i.e. inthe soft photon region we have anomalous Doppler effect and in the hard photonregion we have normal Doppler effect.

Doppler effect in the oscillator radiation process in the medium