On the group velocity of a video signal in a dielectric

It is shown that holomorphic video signals of sufficient duration are capable (as well as holomorphic radio signals of sufficient duration) of propagating in a dielectric without significant distortion at a certain group velocity different from both the speed of light in a vacuum and the group velocity of a radio signal at radio frequencies. It is shown that this group velocity of the video signal coincides with its phase velocity. It is lower than the vacuum speed of light in media dominated by absorption at low frequencies and higher than the vacuum speed of light in media dominated by amplification at low frequencies. The group speed of the video signal in a normal atmosphere is calculated. It is shown that this group velocity is much closer to the vacuum velocity of light than the group velocity of a radio signal at radio frequencies. Therefore, at distances of less than 100 km, it can be assumed that any (including discontinuous) video signal with a duration of more than 10-10 seconds propagates "as in a vacuum" – without attenuation, as a whole and practically at the speed of light in a vacuum.