Does the cat go out?  Maybe he brought in a dead critter.
Do you ever get a mouse in the house?  They have a peculiar odor.  MLB

You can get a black light to check the carpet for urine stains.  I don't
think it would work on vomit so you would have to rely on your nose to
determine where the odor might be coming from.

Celeste

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From: "Girl Jamie" <catnappers75@hotmail.com>

If it doesn't smell like cat pee, it's probably not. As for cat
vomit; Yea, that can smell pretty vile. We had a hyperthyroid
cat that would toss up dinner once or twice a week so I know
the smell of cat vomit (we called them "kitty pukes", it sounds
a little cuter) from 20 ft away. I've got an old Bissell carpet cleaner
that did a good job of getting the smell and stains out of the
carpet. Luckily, the cat learned to run down to the basement
and hack up dinner on the sealed concrete floor, most of the
time, which made cleanup much easier.
If you're smelling cat pee, there's another possibility that drove
me nuts until I figured it out. At certain times of the year, Juniper
bushes smell like cat pee. If you, or nearby neighbors, have a
few Junipers in the yard, you may be smelling them. Here in New
England, they're smelling pretty "catty" right now.

thank you everyone for the good advice.  I really appreciate it!!