Which statement about a discrete-time system is true?

Which statement about a discrete-time system is true?

• A. It is linear if it is time-invariant
• B. It is stable if it is noncausal
• C. It is always non-linear
• D. A causal system's output depends only on present and past inputs

Answer: (D)

Causality is what this question is about. In a discrete-time system, the output at time n can depend only on input values from the present time n and past times (n, n-1, n-2, …). It cannot rely on future values like x[n+1]. Therefore, the statement that a causal system’s output depends only on present and past inputs is correct. For example, y[n] = x[n] + x[n-1] uses only present and past input samples, so it is causal. The other ideas mix up different properties. Linearity and time-invariance are independent: a system can be linear but time-varying, or time-invariant but non-linear (for instance, y[n] = x[n]^2 is time-invariant but non-linear). Stability concerns how bounded inputs map to bounded outputs and does not dictate causality; a system can be noncausal and stable, noncausal and unstable, or causal and unstable. Finally, saying a discrete-time system is always non-linear is false because many systems (like a simple average y[n] = (x[n] + x[n-1])/2) are both linear and causal.

Causality is what this question is about. In a discrete-time system, the output at time n can depend only on input values from the present time n and past times (n, n-1, n-2, …). It cannot rely on future values like x[n+1].

Therefore, the statement that a causal system’s output depends only on present and past inputs is correct. For example, y[n] = x[n] + x[n-1] uses only present and past input samples, so it is causal.

The other ideas mix up different properties. Linearity and time-invariance are independent: a system can be linear but time-varying, or time-invariant but non-linear (for instance, y[n] = x[n]^2 is time-invariant but non-linear). Stability concerns how bounded inputs map to bounded outputs and does not dictate causality; a system can be noncausal and stable, noncausal and unstable, or causal and unstable. Finally, saying a discrete-time system is always non-linear is false because many systems (like a simple average y[n] = (x[n] + x[n-1])/2) are both linear and causal.