I say you could explain away the "analogue" signal by the Borg jamming the communication, or the fact that the line went dead because the ship had been destroyed, leaving only background radiation to lock on to, which, after all is what white noise is.
But with digital video the video codec is decoded digitally and the video artifacts are completely different than analog video artifacts.
The transmission itself is a digital binary datastream.
Since the mid-1990s digital videocameras which convert the video signal to digital for processing and before storing or transmission
became the standard way video was stored and transmitted. Really
That means all of the video would be a digital signal. There is no way it could breakup with analog video artifacts like in BOBW pt.2 unless done in the analog realm before transmission itself.
Since the rise of digital monitors and HDTVs we know that using digital connections like HDMI that the video signals stay in the digital realm from say a Blu-ray disc all the way to the monitor itself which does the conversion back to analog.
One would assume in 300 years from now the monitors would be 'digital' as well and only accept
a fiber optic or binary digital signal over (obsolete) copper wiring.