I dont personally own my own compressor, but I may be able to give you some useful info.

If you want your impact wrench to work to its full potential, then choosing the correct compressor is key. I dont know what your budget is, but they can get up there in cost.(under $1000 to almost $10,000) Of course you dont need the most expensive as those are for shops, but each compressor has stats that should be able to support your impact wrench.
An impact wrench has a recommended air pressure, and air consumption numbers. A compressor has similar numbers. It has max PSI, and air flow @ a certain psi(related to air consumption of the impact wrench).

Now since I dont know everything about this stuff, you may want someone elses opinion as well, but If you want full power, get a compressor that is close to or excedes airflow recommendations for your gun. If not your gun will still work, but not to the maximum torque it claims to put out.