I have a Hummer 3 2008. The radio sounds like its extreamly fuzzy. Is this a antenna problem or speaker problem

Doesn't have a door chime box . Chime sound comes through the driver's door speaker from the radio by the BCM - body control module . What ever problem your having , your best bet , take it to a qualified repair shop .

I seriously doubt it, though there could be a problem with the antenna. See if theres a power antenna fuse. If it's embedded in the glass, look for a broken clip at the window or loose wiring.

Cek the wiring installations for the radio

Static is the antenna. Noise the that goes up and down with the engine RPM's is the condenser on the engine. Fuzzy/cracking noise is a broken speaker.

Sounds far fetched...but there is a good chance that the speakers are bad. In 2008 and 2009 there were some questionable speakers in some gm cars and trucks. If you have doubts...try replacing just one speaker...even if it is temporarily connecting a known good speaker. You may very well find your solution.

Can you be more specific? Did you install the speakers trying to fix it or did the problem start after you installed the speakers?

Here is what I show from the manual.
2005 Hummer H2 Car Audio Installation Guide
Car Radio Battery Constant 12v+ Wire: Orange
Car Radio Ground Wire: Black/White
Car Stereo Antenna Trigger Wire: Gray
Car Stereo Amp Trigger Wire: Pink
Car Stereo Amplifier Location: Under the Center Console or Behind the Glove Box
Left Front Speaker Positive Wire (+): Tan
Left Front Speaker Negative Wire (-): Gray
Right Front Speaker Positive Wire (+): Light Green
Right Front Speaker Negative Wire (-): Dark Green
Left Rear Speaker Positive Wire (+): Brown
Left Rear Speaker Negative Wire (-): Yellow
Right Rear Speaker Positive Wire (+): Dark Blue
Right Rear Speaker Negative Wire (-): Light Blue

It could be a bad amp. Those come with a factory amp usally right behind the radio. Hopefully you can find a used one from a scrap yard. Click Here to search in your area.

Check if any mute function is not activated.

Check your radio and trunck to see if you have a equalizer/amplifier built in or otherwise.Adjustments would cause radio to go into safety mode.Try your balance from side to side.A busted speaker would cause the fuzzy sound or a shorting speaker wire.If none of this is your problem you may need to take it to a sound specialist.