Originally Posted by JohnRoberts
This is 6 of one, half dozen the other,,, subtracting the anti-hum signal from the hot or opposite polarity from the ground will be similar. It needs to be injected at roughly 100% to cancel the hum, so same-same impact for noise and all.
There may be problems with alternate ground connections, but guitars are generally floating.
True, hum and buzz must be of the same amplitude and 180 degrees out of phase with the instrument's hum and buzz.
My point is that if that signal is buffered, you can inject it with less impact on the instrument's sound.
e.g. injecting it with a 100meg resistor on the "hot" terminal after voltage amplification, or injecting it over a 100ohm resistor in the ground line after current amplification.
The circuit could be battery powered (floating) and referred to the guitar's ground.