Problem 2

Fill out the table of unilateral Laplace transforms below (all signals are defined on the interval

t € [0, 0)). Also state the region of convergence (ROC).

Signal, g

ROC

ελέμ(t), λεσ

e(t-thi) (t-tshift), AEC, fshift > 0

text μ(t), XE C

eat cos(wot)μ(t), o ER

et sin(wot)u(t), o ER

Σμ( -- kT), T > 0,

k=0

Laplace transform, ĝ

Remark: The last signal is a "staircase" function in which a "step" occurs every T seconds. It is

useful to sketch it to see what it looks like. A closed-form expression for its Laplace transform can

be determined using the geometric series summation formula when 8 € ROCg.

3