A history of the phenomenon of fast oscillations of amplitude and momentary frequency of a signal (pulse) propagating in dispersive media is presented. This history is divided on three periods: first, from its discovery in 60-th of XX Century, second, its oblivion up to the end of XX C., and third – its open discussion from the end of XX C. to present days. A theory of the analytical signal is critically discussed. Some unpublished results are presented.