My goal is similar, but my code is quite different. The noise in my hardware configuration comes from the USB power coming to the Uno. When I use batteries the noise is gone. I can literally detect a pin drop. I have noticed that it is much more sensitive to low frequency noise. A heater rumble in the basement or truck driving by miles away completely overpowers anyone talking in the next room. I know how to write a high pass filter, but I think it's pretty cool the way it is!