Before you all go to all sorts of efforts to eliminate the noise, it might be worth the effort to take a digital volt meter and do a few simple checks. Put the meter in the DC meter scale and measure the voltage with the engine off and not having run the engine for a while. Your looking for the at rest battery voltage. I would expect it to be about 12.5 volts or so.
Next, start the engine and measure the battery voltage again. You should see something like 13.8 to 14.3 volts or so.
Next, turn on the headlights and again measure the battery voltage. It should be near the same voltage as when you first started the engine. Now put on the high beam headlights. Measure the battery voltage. You may see a slight voltage drop from just the low beam headlights.
The next test is to now turn on the heater or air conditioner with the high beam headlights still on. here is where the good alternator and a bad alternator will part the voltages. If the battery terminal voltage has dropped down much, I would expect that you have a bad alternator.
While we are at max load, change the digital volt meter to the AC range and go into the milivolt range. Again place you meter across the battery terminals. You should not see very much in the order of an AC voltage with a good alternator. If you have a shorted diode in the alternator, I would expect to see a reading over about 30 to 50 milivolts.
As others have mentioned, you need to make sure there is a good ground wire going from the negative post of the wiring to the vehicle frame. You should also have a heavy wire going from the negative side of the battery to the starter and or the engine itself.
You can sort of keep an eye on the status of your alternator by watching your headlights at night. If you pull up to a stop sign or traffic light and the lights dim way down, your looking at a problem. The get brighter as you start up from the dead stop.
Another issue is if you battery is about 3 years old or more, Your living on borrowed time. As soon as it gets cold, you won't start the engine. Batteries have a useful life of about 3, maybe 4 years. The internal resistance starts going up and their capacity to provide a bunch of amps goes down.
I buy the largest battery that will fit into the battery holder when I change out my vehicle battery. Being in the radio field for some 45 plus years, I always have radios in my vehicles. Generally it's on the first cold morning that I find out just how good my battery is to me. Have had to change out a few alternators in the various vehicles I have had over the years. The first sign is the alternator whine. Another sign is the clock looses time and resets to midnight when you start the engine.
Hope this provides some clues on your search for the problem.