DSP in general is very tough, almost like magic. In music technology I see people doing some crazy things but a lot of the source code is closed and going through textbooks of material (mostly hard maths) is painfully slow. I’m still trying to find a way to convert a low pass like that into a high pass… Maybe this might help. One pole, one zero LP/HP — Musicdsp.org documentation
Soft saturation is really easy to implement but we don’t really need it - it’s a contrast enhancement. It’s a specific kind of waveshaper, and we already have that thanks to the curves graphs. A compressor isn’t as easy to make but it would have a very unusual effect.
We should note that we’ve got an advantage that musicians don’t: our signals aren’t live and we already have all the data we need. We don’t have to care about latency, so we can take samples anywhere within the image.