Either the timing or the fuel mixture is out, but either way I wouldn't drive the car when it's doing this. Backfiring is really bad for a modern car and it indicated a major fault with the car's ECU.
Take it to a garage, preferably an Alfa specialist.
Sounds like the timing is out. As this is an ecu equiped model and the ignition timing is not adjustable i would suspect that the cam timing is out. The alfa 1.8 twin spark has a unit called a variator bolted to the inlet cams timing belt pulley. These are used to alter the timing automatically on the inlet cam. These do wear out and can make a noise also.
Obviously this is a guess over the internet the car will need an check over. You should find an alfa specialist as this will save you money in the long run.