https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwj5jN71mNz1AhUlzzgGHUDYBM4QFnoECBIQAQ&url=https%3A%2F%2Fx-engineer.org%2Flinearization-linear-approximation-nonlinear-function%2F&usg=AOvVaw01n7Mj7NMHztiWkn-CAZ_3

Something like:

x = sgn(y- y1) + delta(y)*X

with sgn between 0 and 1, y1 =200 and X in [0,1]. Otherwise, you can try with a logistic function if you want something smoother.

I wouldn't bother as it should be considered an attempt to curve noise.

I would bother to determine whether the data is actually noise or hides several different and summed curves.