The impulse response h[n] of a linear time-invariant system is given by h[n] = u[n + 3] + u[n – 2] – 2u[n – 7], where u[n] is the unit step sequence. The above system is

The correct answer is: B. Stable and causal

A causal system is a system that responds to an input only at times that are after the input is applied. A stable system is a system that does not amplify its input signals indefinitely.

The impulse response of a linear time-invariant system is the output of the system when the input is a unit impulse. The impulse response of a causal system is zero for negative time, and the impulse response of a stable system is absolutely summable.

The impulse response of the system in the question is $h[n] = u[n + 3] + u[n – 2] – 2u[n – 7]$. This impulse response is zero for negative time, so the system is causal. The impulse response is also absolutely summable, so the system is stable.

Therefore, the system is stable and causal.