For a causal continuous-time LTI system, where is the ROC relative to its poles?

• A. The ROC is to the right of the rightmost pole.
• B. The ROC is to the left of the leftmost pole.
• C. The ROC includes the imaginary axis.
• D. The ROC is the entire complex plane.

Answer: (A)

For a causal continuous-time LTI system, the impulse response exists only for t ≥ 0, so its Laplace transform converges in a region of the complex plane that must lie to the right of all poles. Each pole contributes a term that behaves like e^{p t}, and for the integral defining the transform to converge as t → ∞, the real part of s must exceed the real part of every pole. This makes the region of convergence a vertical half-plane: all s with Re(s) greater than the largest Re(pole). In other words, the ROC is to the right of the rightmost pole.