Just food for thought, isolation transformers work on the idea of induced voltage. First core is powered from your home the second core has its voltage induced keeping everything you plug into it seperate from the "dirty" power supplied to your home. They are fantastic for sensitive equipment. However if this is a plug in unit (three prong) the ground is not isolated from your home and that can act like a big antenna( all grounds in a home ideally are all connected in a panel together) every switch and outlet has a ground. Also dc voltage cannot be transferred from the isolated coil back out to the street and it is not regulated into ac sine wave (also a reason for a iso transformer to prevent all but correct voltage getting to your equipment). So while it likely wouldn't matter even slightly in your case , trace dc voltage can get back onto these coils sometimes and cause harmonic issues, usually this would happen in office buildings with a decent amount of computers. The radio station pick up though could be due to the grounds in your home. To find out if it is the case try taking the outlet you are plugging into out of the wall and remove the ground wire, then put a new wire from that outlet directly to the dirt outside of the home. Of course shut the breaker off first. You could also just remove the ground and see if it goes away before you run the wire. It is not safe to leave it that way though. There is a correct method if this is the problem to fix this by code standards. What I mentioned would just be to test.
Regards,
Bill
Regards,
Bill