# The impulse response of a LTI system which is continuous is H (t) = e^-|t|. The system is ___________

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The impulse response of a LTI system which is continuous is H (t) = e^-|t|. The system is ___________

(a) Causal and stable

(b) Causal but not stable

(c) Stable but not causal

(d) Neither causal nor stable

The question was posed to me in class test.

My query is from Region of Convergence in chapter Laplace Transform and System Design of Signals and Systems

by (42.1k points)
The correct choice is (c) Stable but not causal

For explanation I would say: For t<0,

H (t) ≠ 0

Therefore the system is not causal

Again, $∫_{-∞}^∞ | h(t)| \,dt = \frac{1}{3}$ < ∞

∴ The system is stable.

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