Not only will an arduino not be able to do this, but I believe that a digital tv tuner will not be able to capture " all digital T.V signals at the same time". Not even close. The amount of data you are talking about here is rather a lot and you will need some serious power for matlab to be able to even load the data, let alone process it.
According to wikipedia
Each commercial broadcasting terrestrial television DTV channel in North America is permitted to be broadcast at a bit rate up to 19 megabits per second.
How many channels were you thinking of capturing "at the same time"? A dozen? That's a quarter of a gigabit per second. To think that a single-threaded 16Mhz processor could deal with this is to have a seriously wrong idea about the scale of what you are asking. You might as well be asking for a car jack that can move a railway bridge.
What are you actually trying to do?