Question

The below diagram shows the pole-zero plot of a continuous time system

The system is stable and non-casual for the ROC

• A. -3 < Re(s) < - 2
• B. Re (s) > 2
• C. Re(s) < 2
• D. -2 < Re(s) < 2

Answer 1

The correct option is D -2 < Re(s) < 2

For an LTI system to be stable, the ROC of the system function must be the imaginary $\left(j\omega \right)$ axis.

Here the only ROC which contains imaginary axis is -2 < Re(s) < 2.

LTI system is casual, if ROC is to the right side of right most pole.

$\therefore$ System in non-causal for -2 < Re(s) < 2 and -3 < Re(s) < -2.