right...I'll bet the waveform of a .380, like someone suggested, never gets altered as it bounces around off of the sides of buildings and the occasional tree.
You're right, it does, but the systems are that good. Honestly, this technology isn't that amazing.
If you think about how digital signal processors, a very "mature" technology since the late 70's early 80's started with things like digital phone calls and CD music, then extrapolate advances that kept pace with the rest of the microprocessor field, the state-of-the-art capability to record and analyize audio information is very advanced.
When you think about how computers and software are capable of things like transcribing human speech with 95% accuracy or better that's commercialy availible for a few dollars, or other tasks like robust facial recognition systems that can function from various angles, and even not be fooled by things like glasses and beards, analyizing audio information for gunshots, and ignoring false positives like firecrackers and backfire is almost trivial.
Determining actual caliber and some general information about the firearm such as barrel length isn't out of the question either.
Since things like buildings and trees don't move very often, echoes will be consistent and may even enhance accuracy. Besides trigangulating the arrival of sound between three or more microphones, echoes can actualy help, since the number of combinations echoes can take between buildings before reaching the microphone is almost infinite, but when you know where the surfaces.that can provide the echoes are, it can be like a fingerprint.
I don't doubt the efficacy of such audio systems at all. I just doubt the efficacy of the police, and ultimately, the politicians they answer to.