Definition of a CT LTI system
if $ \,y(t)=Cx(t) $ where C is any constant, then
$ \,h(t)=k\delta (t) $
Example of Laplace transform
Use the definition of laplace transforms to convert an h(t) function to an H(s) function:
$ H(s)=\mathcal{L}\left \{ x(t) \right \} \ = \int_{-\infty}^{\infty} h(t) e^{-st}\, dt $
if our system is $ h(t)=k\delta (t)\, $
