I would be very surprised if you could figure out a way to reliably discriminate between the sound of a gunshot and the sound of a car backfiring given that they're basically the same thing (that is, the sound of a gas rapidly expanding in a metal tube).

Yeah, well you'd be wrong. Anyone who's spent time around guns would instantly recognize the difference, and training a computer to do the same thing isn't even hard, it just takes a lot of patient work.

The most important difference here is a gun is pushing a projectile out and a car isn't.

Differentiating between cap guns, starter pistols and fireworks might be a little more hazy, but it's still not the same thing as a backfiring car.

Sure that's the case when you're firing guns and backfiring cars across an open field from whatever you're measuring sound with but sounds tend to get screwed up when distance, obstructions and white noise are added.

You make it sound like people have never had to do signal analysis before.

Have you seen what NASA can do with images?