Imagine transfer function obtained by Laplace transform, for example:
$G(s) = \dfrac{1}{s+1}$
Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider this operation valid for this example).
What is the unit of the $\omega$? So far what I have seen, the $\omega$ is noted as frequency or angular velocity. I asked my colleagues and I got various answers:
- rad/sec
- Hz
- no unit
What is correct and why? Does it depend on real variable passed to transform (if somebody uses different variable than time)?