What kind of transform is used in this picture?

Question

What kind of transform used in the following picture?

I think this is some kind of compression method, but I'm not sure.

Answer 1

For the second curve,

$$y=\tfrac13 \text{round}(3.5\cos(\tfrac{x-65}{10}))$$

gives a rather good fit, where "round" is the "closest integer" function (Examples: round(0.7)=1, round(3.4)=3, round(-2.7)=-3).

I have no idea for the third and fourth graphical representations.

Answer 2

This image from book Discrete Time Signal Processing Edition 3.

Same image from 2nd edition, page 195