Was the modem/router provided by your ISP?
Do you have access to its configuration settings?
USRobotics website shows that the modem/router has very good statistics/logging capability as well as diagnostics, (there's even a nice interactive demo).
Log into the modem now, go to the Status tab and hit the Reset button on the WAN, ATM & ADSL Statistics pages.
The next time it happens, log into the modem, go to the Status tab and look at the System Log and WAN, ATM & ADSL statistics - take screen captures.
Under the ADSL Statistics tab perform a ADSL BER Test and take a capture of the results.
Under the Device tab there is a Diagnostics function, run both test when it happens, capture the results.
Please post them back here. I'm not saying any of this will definitively isolate the problem but it should help us understand a bit better.
In the meanwhile, it should cost nothing, (well here anyway), for your physical line provider, (copper cable - BT, etc), to perform a remote test on your phone line - ring them up and say your getting intermittent noise on the line.
Also, is the phone working normally when it happens, ie. dial tone, no noise (crackling, etc).
If it's happening often enough, disconnect ALL other devices connected to the phone line, (and I mean ALL
- phones, filters, external bells, fax machines, alarm monitoring equipment, etc) - this is the
most basic test and will help isolate it to either the modem/phone line or
something that's influencing them.
may help, specifically from here
on. gexecuter's fault turned out to be faulty wiring, (loose wire), from his house to the external connection at the pole - which the signal ratios pointed/hinted at.