In effect analyzing the tool would look at the hum and create a filter
that matches it exactly. I guess there's a word for that?
Yep noise reduction;) In this case Hum/Buzz Removal.
I havent found a good tool for it in Linux yet myself, though you can
give audacity's noise reduction a shot, I tend to have bad luck with it
as it removes to much IMO.
There are VSTs that will do this if that is an option for you, or other
programs as well, though not nessecarily on Linux(Audition on Windows
has a decent noise reduction for example and is less exxpensive than
many VSTs for that purpose)
Seablade