Compressor Problem?

The refrigerator and freezer are still working fine, but the volume and duration of noise produced when the unit starts up has increased significantly in recent weeks. There is a loud, deep buzzing noise when the unit starts a cooling cycle. This noise fades to a normal (quiet) mechanical hum after 20 to 30 seconds. I suspect this may indicate the compressor is struggling and may not last much longer, but I’m no expert. I would like to know if this is the problem, if its worth replacing the compressor in this old unit or should I spend the money on a new fridge? Thanks.