There are two places you mainly get electrical noise from a car, alternator and ignition system. Unplug your alternator so you are running off battery only and see if the noise is still there.
There are noise reduction caps on your alternator, coil and if your car has points then in the distributor cap. Try replacing those, they look like a little cylinder with a fly lead on it.
If the above fails you can make a simple circuit to filter out noise.
Get two diodes above 1 amp, IN4004 will do, tie the ends with the stripes together this joined end is your supply +12V. With the other ends, one goes to ground and the other to your +12v supply from the car.
Now you need to get some capacitors to filter the noise, the hard part is going to find what value to use. The higher the Uf value the lower the frequency of noise it will cancel out. I would suggest buying a handful of caps from 220 Uf to .01 Uf, just make sure they are rated over 12v. Try each one by joining it to the +12V supply (after the diodes) and the other end to ground (some caps have polarity + goes to + and - goes to ground, the ones not marked it does not matter).
Find what cap value does the most good and get more around that Uf value, it does not matter how many caps you have in parallel.