Laplace Transform of Step and Ramp

Cuthbert Nyack
To find the Laplace transform F(s) of a step function f(t) = 1 for t 0. Substitute f(t) into the definition of the Laplace Transform below.
This gives the following:-
For a unit step F(s) has a simple pole at the origin.
To find the Laplace transform of a unit ramp f(t) = t for t 0. Substitute f(t) to give:-
Integrating by parts and evaluating gives:-
For a unit ramp F(s) has a double pole at the origin.
Return to main page
Return to page index
Copyright 1996 Cuthbert A. Nyack.