Which statement correctly describes the relationship between stability and the ROC of a Laplace transform for a causal LTI system with an absolutely integrable impulse response?

Which statement correctly describes the relationship between stability and the ROC of a Laplace transform for a causal LTI system with an absolutely integrable impulse response?

• A. The ROC must not intersect the imaginary axis.
• B. Stability is unrelated to the ROC.
• C. The ROC must include the imaginary axis; for a causal LTI with absolutely integrable impulse response, the ROC includes the imaginary axis and lies to the right of all poles.
• D. The ROC is always the entire complex plane.

Answer: (C)