I was going to take a pic of the secondary air pump location on my 1.8t (AUQ) engine but its difficult to see.
If you stand at the front of the car, look at your dipstick tube then look down and slightly left (your left/towards drivers side), at the very bottom there is a black pump, i will try and find a pic of one because you wouldnt know what it was without seeing one prior.
Try and see if thats where your noise is from.
Ok found this pic which is a view from underneath, is on a VW but is ok
Pic the location is the same on my engine at least, the pump is the whole unit that has the bolts circled on. You could maybe try and get your undertray off and then start the car so you can get right at it to listen.