Pumping type noise at idle?

I have a 2012 Jetta Sportwagen TDI that has had this issue since I bought it, but I'm not sure if its normal or not. It has the 6spd DSG, and has been having some issues related to the transmission being jerky like a kid who doesn't know how to drive manual well yet when it is cold at times.

https://www.youtube.com/watch?v=Yg8wRcOe-2Y

Here is the link to the video of the idle noise, its most noticeable with a good pair of headphones while I am in the drivers seat, and before I open up the hood and look around for the video. Any help would be greatly appreciated.

I hear it. My Mk7 makes the exact same noise, has for 35,000 miles, and has a regular manual transmission. I don't know what it is. In person, it sounds like an out-of-true pulley.