Topic: Signals and Systems
Which of the following systems is "not" causal?
- A. $h[n]=\delta[n]$
- B. $h[n]=u[n]$
- C. $h[n]=\delta[n]+\delta[n+1]$
- D. $h[n]=(0.5)^{n}u[n]$
Answer: C. $h[n]=\delta[n]+\delta[n+1]$
Explanation: A discrete-time linear time-invariant (LTI) system is causal if and only if its impulse response $h[n] = 0$ for all $n < 0$.
Looking at option (c), $h[n] = \delta[n] + \delta[n+1]$. If we evaluate this at $n = -1$, we get $h[-1] = \delta[-1] + \delta[-1+1] = 0 + \delta[0] = 1$. Since $h[-1] \neq 0$, the system anticipates future inputs and is therefore non-causal.