Well not true... some cheap one like that unfortunately. If grounding like others suggested cannot solve, you can use noise suppressor on the +ve power supply. It is just heavy inductor and can be made by winding heavy enameled copper wire on toroid core.

Good luck

I presumed that you buy a set with standard mounting everything. You get it installed at a shop? Did you buy from that shop too? Then the shop probably don't have much technical knowledge. I think car audio accessory shops have this noise suppressor.

Normally the body of the radio is screwed to the car chassis. This is the grounding and this is also the -ve (negative) power supply. Only +ve (positive) wire goes to the radio and usually comes with the fuse. The good contact is important (thus called good grounding) to prevent this humming noise.

My old car last time I have the same problem with the radio (well cheap also ) Believed that the noise (like you heard, louder when you step on gas pedal) entered the radio through power supply line., I tried to put an inductor at the +12V power wire near the radio. It reduced a bit. Maybe the inductance wasn't enough. Since I had an unused transformer, I connected the secondary side to act like filter and the noise gone. Well this is not professional. You need to make sure the wire gauge can carry enough current for the radio to operate at full capacity.

The filter need to be installed as close to radio as possible. Probably just put behind the radio in dash cavity there. I don't know if you have any electronics knowledge but I suggest you ask someone who knows to brief. It is simple to understand. Maybe can ask other shop that know how to solve the problem, but they probably want you to replace the radio you had

This is good if you have separate amplifier too but I'm not sure in your case. Normally the cheap car stereo is just like the mini compo, give high power rating but actually it is not RMS rating. So quite meaningless. Therefore I presumed that the car audio is just 1 single unit.

Noise can be from several source. Maybe this article can give you something to work on. I would say power noise suppressor is not expensive. I guess should be less than RM50? I have no idea

http://www.crutchfield.com/S-vjpyGXYfAS0/l.../car/noise.html