What is an easy way to remove the negative portion of a signal without distorting the positive side of it?
I would recommend a precision rectifier.
The most basic op-amp circuit (it has to be the right op-amp of course) is this: -
It relies on a few special features of the LT1078 but is a pretty good half wave rectifier.
You can use most op-amps in this configuration: -
The cool thing about this circuit is that one op-amp can produce two outputs.
Note that both the op-amp circuits shown above are inverting configurations but that doesn't matter if you are dealing with waveforms that are amplitude symmetrical.
You can also make full wave rectifiers using two op-amps: -