Question 1 (30 points): Laplace Transform
The pole-zero diagram of an LTI system and its input are given in Fig. 1. It is know that
x(t) is a right side signal.
For x(t)
For h(t)
-C2
C4
-C4
σ
-1/C4 1/C4
-1/C4 1/C4
Figure 1: Pole zero diagram of LTI system, h(t) for Q.1
We know that $H(s)|_{s=0} = 1$ and $X(s)|_{s=0} = 1$.
(a) (5 Pts.) If it is known that $h(t)$ corresponds to a stable system, determine the ROC
of the system and $h(t)$.
(b) (5 Pts.) If it is know that $h(t)$ corresponds to an unstable system, determine the ROC
of the system and $h(t)$.
(c) (5 Pts.) If it is know that $h(t)$ does not exist, determine the ROC and comment on
why $h(t)$ does not exist.
(c) (15 Pts.) For a causal system, determine the output in time domain and its RoC.
