From my experience the best way to minimize the background noise is to try with different power supplies. For me, my old iPod charger is the best one over a good Line 6 power adapter or over feeding Arduino directly from the laptop.
You can have a look to the "
Powering Arduino Due" topic for additional info.
The low hiss in Arduino is due to the noise in the ADCs, you can check with some pedals like the
sinewave generator or the
Dirty Synth which do not use the ADC that there is no noise at all.
How to reduce the noise in the ADCs is a
hot topic in the Arduino community:
There is a great article by djerickson "
Evaluating Arduino and due ADCs" and he suggest that
"Most Arduinos default to using VCC as the ADC reference. If the VCC is 5V, then it either comes from the USB connector or from the voltage regulator" - "Adding a more precise voltage reference to an Arduino isn't hard. Pay a few dollars, and connect a 2 to 4.5V (3.3V max on the Due) reference source to the reference pin, and set the Arduino to use external reference with analogReference(type). Compared to VCC, this will provide better accuracy, noise, and stability. "
There are other approaches like using oversampling, filtering the input (software filter) or using a different software ADCs setup that might reduce this hiss.