The signal x(t) = u(t-1) - u(t-3) is the input to an LTI system with the impulse response h(t) = u(t-5) - u(t-8). the system is initially at rest.
a) Compute the output y(t) of this system using convolution.
b) Compute the output y(t) of this system using the Laplace transform.
The Attempt at a Solution
a) I got the answer to be
0, t <= 6
2, 6 < t <= 8
1, 8 < t <= 9
2, 9 < t <= 11
0, t > 11
b) I have no idea how to compute the laplace transform of unit step functions. any help?