I had a listen to the clip and there is quite a bit of hum on there which lead me to think that it might be an ground loop issue, personally i would test removing the ADA8000 from the rack completely and also the input/output cables so that there is no other possible ground connection than the ground from the powerplug present.
Also be sure to have all equipment connected to power at the same point as closely together as possible, if you connect one piece to one wall power outlet and another to the wall outlet a few meters away it may make a big difference since there might be quite large differences in voltage potential between outlets.
Try and test if you get these noises after you have done this and the noise is gone then you can add connections, mount it in the rack step by step and test if these are the cause of the noise.
One other possibility is that this click noise is due to digital distortion at some stage, the hum noise seem pretty high in the recording, maybe it is causing digital clipping somewhere which also sounds like that.
If you are in Europe like me or another place where you can turn the power connector 180 degres it might be something to try doing this on the different pieces of your equipment one by one.
Oh, and if you use a laptop the powersupplies are known to cause problems with groundloops, try running on battery as a test if you have a laptop. I have had this problem myself.