Partial Even Harmonic Distortion?

Hi, I’m attempting to simulate the strange distortion that these sirens have. The speaker drivers are compression drivers.

Voices have a weird buzzy like tone above the base frequency.
voice.PNG
The actual siren tone is a square wave, but the distortion adds harmonics that make it sound different.
tone.PNG
I have tried things like a highpass(1000hz)+half wave rectification, it makes the square wave sound ok, but the voices sound off.
I also tried a slew rate limiter E.X. “snd-congen track 0 (/ 1.0 4000))”
But it still sounds off, and adds harmonics below the voice’s base frequency.

Any help?

Thanks,
Elijah

Your question is too open ended for a precise answer.
Maybe you would find something useful in one of these topics:
https://forum.audacityteam.org/t/tone-generators-siren/40272/1
https://forum.audacityteam.org/t/need-help-with-gverb-making-a-siren-effect/20498/1

Here, I’ll provide an example of what I am talking about.

I made this plug-in: https://www.youtube.com/watch?v=JtaJ2I0c5AY

(not trying to self advertise!)

AudioThing’s “speakers” plugin has a PA-horn emulation …
audiothing's speakers demo PA-horn.png
The free demo version inserts silence every ~30 seconds, (maybe long-enough to complete some jobs).