Differentiable approximation of the round() Matlab function

Question

Could you possibly suggest a differentiable approximation for the round Matlab function?

The round function looks like this:

I would like a differentiable function which [closely] resembles the one in the figure.

Answer 1

You could write the derivative using the dirac delta - it's called 'dirac comb'.

Also you can write the round function as sum of the Heaviside step functions.

for both there are many approximations - just select a differentiable one.