# Approximation of Saturation function

"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1)

The context where I encountered this is LTI (linear time-invariant) system analysis (in classic control theory).

I tried to take its laplace transformation and mix it into the system's transfer function as usual, but soon figured out that I can't perform the inverse laplace transformation once it's mixed in.

Fortunately, an analytically accurate solution is not necessary. So I figured I need a simple yet effective function that does pretty much the same as clip(x), with a simpler Laplace Transformed form.

Or... Are there any simpler ways of doing it (other than doing an discrete-time simulation)?

clip() is not a LTI filter (it's not linear). So I don't understand how you'd expect to use Laplace/Fourier here.