Question

The ROC of the Laplace transform of a causal signal lies

• A. Left of leftmost pole
• B. On imaginary axis
• C. Between poles
• D. Right of rightmost pole

Hint:

ROC for Laplace transform: \[ \boxed{ \begin{aligned} \text{Causal signal} &\rightarrow \text{Right of rightmost pole} \text{Anti-causal signal} &\rightarrow \text{Left of leftmost pole} \text{Two-sided signal} &\rightarrow \text{Between poles} \end{aligned} } \]

Answer 1

The Correct Option is D

Step 1: Recall the ROC property for causal signals. For a right-sided (causal) signal, the Region of Convergence (ROC) extends to the right of the rightmost pole in the \(s\)-plane.

Step 2: Identify the correct option. Hence, \[ \boxed{\text{ROC lies to the right of the rightmost pole}.} \] Therefore, \[ \boxed{(D)} \] is the correct answer.