Cats are carnivores that feed on mostly high protein-rich foods. This type of diet produces intensely stinky gas because proteins are known to contain a large amount of sulfur which is a particularly odorous chemical.
Cats' farts are mostly silent, but the odor is unbearable. The reason that their farts are so rarely audible is because the amount of gas they produce is much smaller, but dense and highly concentrated. When cats release gas, their gastrointestinal system has low internal pressure thus the gas comes out slowly and steadily. The muscles on their bottoms don't close as tightly as that of humans, so it produces less sound, but the most interesting fact is that cats are a lot more relaxed when they fart because passing gas is a norm to them as opposed to an embarrassing moment.
(Now you know the below cat fart video is FAKE)
According to a veterinarian, if cats fart audibly, it could be an indicator of pathology.
So next time when you smell something foul, but cannot quite make out what it is. Check with your cat and see maybe it's time for him to go potty :-).