The impulse response h[n] of an LTI system is

h[n] = u[n + 3] + u[n - 2] - 2u[n - 7].

Then the system is:

1. Stable

2. Casual

3. Unstable

4. Not casual.

Which of these are correct?

Concept:

• LTI system is causal when h[n] = 0 for n < 0
• LTI system is stable when \(\mathop \sum \nolimits_{n = - \infty }^\infty \left| {h\left[ n \right]} \right| < \infty \) i.e. It should be absolutely summable.

Calculation:

h[n] = u(n + 3) + u(n – 2) – 2 u(n – 7)

∵ h[n] ≠ 0     n < 0 ….. system is Non causal

\(\mathop \sum \nolimits_{n = - \infty }^\infty h\left( n \right) < \infty \) i.e. given impulse response is summable hence it is stable.