What does ROC Mean?

1. Sep 23, 2016

jaus tail

1. The problem statement, all variables and given/known data
Find laplace of e-atu(t) where a > 0

2. Relevant equations
Laplace is integration from -inf to +inf f(t)e-stdt
u(t) is 1 for t more than equal to 0.

3. The attempt at a solution
Well i got the answer as X(s) = 1/(s+a).

But the book said something like ROC like region of convergence and for that s must be more than -a
I understand that s more than minus a, gives positive 1/(s+a)
but why?

Why can't ROC be negative? What does ROC mean? I am studying Signals and Processing.

2. Sep 23, 2016

Staff: Mentor

3. Sep 23, 2016

LCKurtz

Your integral is $\int_1^\infty e^{-st}e^{-at}~dt = \int_1^\infty e^{-(s+a)t}~dt$. That integral will only converge if the exponent is negative, meaning $s+a>0$. ROC in this case means the region of convergence, the values of $s$ for which the transform is defined.