engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Laplace Transform Properties of Region of Convergence of Laplace Transform
A real signal x(t) has Laplace transform X(s) and
1) X(s) has exactly two poles.
2) X(s) has no zeros in the finite s-plane.
3) X(s) has a pole at s = -2 + j
4) e3t x(t) is not absolutely integrable.
5) X(0) = 3
Then X(s) is:
1
\(\rm \frac{{10}}{{{s^2} + 5s + 4}};~ROC:Re\left\{ s \right\} < - 2\)
2
\(\rm \frac{{10}}{{{s^2} + 4s + 5}};~ROC:Re\left\{ s \right\} > - 2\)
3
\(\rm\frac{{15}}{{{s^2} + 4s + 5}};~ROC:Re\left\{ s \right\} < - 2\)
4
\(\rm \frac{{15}}{{{s^2} + 4s + 5}}; ~ROC:Re\left\{ s \right\} > - 2\)