I do not happen to have a fax machine on that line--it just rings and I hear those "fax" sounds. I called Bell South and demanded that they tell me who was waking me up, but they told me I had to spend money on a lawyer to find out who was using Bell's lines to call MY phone.
Chances are your modem has a fax capability. You may even already have fax software on your hard drive, and if not, there are plenty of fax programs you can download for free. Then you can just leave the program running at night, let it pick up and receive the fax, and voila, you'll know who's calling. Then you can file a complaint with the FCC.
BellSouth sucks. Our line drops at least 15 times a day when I am on the internet conducting business. The clients are becoming really pissed. I found out that we have fiber optic lines at the street (we just built a bran new house in a private subdivision with all underground utilites) BellSouth refuses to put in the network, allowing us DSL high-speed broad-band communications.
Can you turn off the ringer on your bedroom phone before you go to bed?