Question

Which of the following system is causal?

• A. \( h(n) = n \left( \frac{1}{2} \right)^n u(n+1) \)
• B. \( y(n) = x^2(n) - x(n+1) \)
• C. \( y(n) = x(-n) + x(2n-1) \)
• D. \( h(n) = n \left( \frac{1}{2} \right)^n u(n) \)

Hint:

Causal systems never depend on future input: no \( x(n+1), x(n+2), \dots \)

Answer 1

The Correct Option is D

Step 1: A system is causal if output at time \( n \) depends only on present or past inputs (i.e., no future values like \( x(n+1) \)).
Step 2: Analyze each:
(1): \( u(n+1) \) implies signal exists for \( n = -1 \), so may not be causal.
(2): Has \( x(n+1) \) — future value → non-causal.
(3): \( x(-n), x(2n-1) \) → includes future values for some \( n \) → non-causal.
(4): All terms depend on present/past (due to \( u(n) \)) → causal.