The high voltage is applied across the tube, the voltage varies depending on the lamps and type of ballast.
The filaments are located in each end of the tube and are connected between the two pins on the end of the tube. They do not operate off high voltage but have something have 4 or 5 volts across them. In a typical rapid start set up the filaments heat the gas in the tube until the high voltage is able to start an arc across the tube. This is the orange glow you sometimes see if a lamp doesn't start right away.
Instant start ballast do not heat the filaments, they use an higher voltage to strike an arc on the cold lamps, but most lamps still have filaments in them.
When you rewire a light for LED tubes, you wire line voltage to the two pins on one end of the lamp that would have connected to the filament.
Back on topic there are a myriad of 4' led replacement tubes that can be brought up with a quick search.
Here is some that I have used
http://keystonetech.com/all-products/linear-led-tubes/direct-drive-led-t8/ You should look at the 18 or 22w.