# Clamp function transfer function

I feel like this should be simpler than I'm finding it, but here goes. I need a transfer function for the function y(t)=u(t)H(u(t)-m)(1-H(u(t)-M)). This is the simplest way I could think to represent a clamp function, with max value M and min value m. As per usual, u(t) is the input, y(t) is the output. Thanks in advance for any help!

Edit: H(x) represents the Heaviside function (0 if x<0, 1 otherwise)

• What is H and are there some missing/misplaced parentheses in the equation provided?
– AJN
Apr 25, 2023 at 0:35
• @AJN Edited to add this info, but H is the Heaviside function and as far as I can see there are no misplaced parentheses, however I did mean to have a -m in a different place, so it is now correct. Apr 25, 2023 at 13:04
• This looks like "clipping" as described in signal processing. I don't think it has an easy laplace transform as might be the case for instance with a window like $$y(t) = u(t)H(t-t_{min})[1-H(t-t_{max})]$$, so getting a transfer function directly might not be possible. It may be more appropriate to model the behaviour in simulation within the wider design problem rather than finding an analytical solution. Is there a wider context that you need the solution for? Apr 26, 2023 at 10:58
• I'm using this for a physical control system - the clipping can be implemented as code. I was mostly just hoping to get a transfer function to simulate this easier. Apr 26, 2023 at 15:44
• What you describe is nonlinear. A transfer function can only represent linear systems. Apr 27, 2023 at 8:59