The head and amp are full of transistors, if one of them has failed, or some other component, it is time for a new head or amp.

Now,
If you have good sound from all other speakers, then power and ground to the head and amp are fine, so we know the problem is with the amp, head or speaker.
It if CONSISTENTLY works after "warming up", then we have a component failure in the amp or head unit.

In any event, the only way I know of to track this down is to swap left to right conections between the head and the amp. If the problem moves to the other side of the car, the problem is in the head. If it stays on the same side, it is amp or speaker.

It the speaker is truly buzzing (continuous rate of buzz) the problem is NOT in the speaker. If the "buzz" is varying with the music, it COULD be a bad speaker, but from your descriptoin, I dont see that. Here is a question: There are TWO door speakers, do they both make the same noise? If so, and I'm sure they do, then it certainly is not the speaker(s).