Question

The impulse response of a continuous time LTI system is \(H (t) = (2e^{-2t} -e^{\frac{t-100}{100}}) \,u (t)\). The system is ____________

(a) Causal and stable

(b) Causal but not stable

(c) Stable but not causal

(d) Neither causal nor stable

This question was addressed to me during an online interview.

Query is from Properties of Systems topic in division Signals and Systems Basics of Signals and Systems

Answer 1

The correct option is (b) Causal but not stable

For explanation: For t<0, h (t) = 0.

Therefore from the definition of causality, we can infer that the system is Causal.

Now, \(\int_{-∞}^∞ |h(t)| \,dt = ∞\)

∴ From the definition of stability, we can infer that the system is unstable.

Hence, the given system is causal but not stable.