Problem 2.29, HW3, ECE301, Summer 2008

Find if each system is stable and causal.

A

h(t) = $e^{-4t} u(t-2)$

u(t-2) = 1 for t >= 2 making h(t) = 0 for t < 2. The system is causal.

$\int_{-\infty}^\infty e^{-4t} u(t-2) = /int_2^\infty e^{-4t} < \infty$. Therefore the system is stable.

This system is stable and causal.

B

h(t) = $e^{-6t} u(3-t)$

u(3-t) = 1 for t<=3, making h(t) $\neq$ for t < 0. The system is not causal.

$\int_{-\infty}^\infty e^{-6t} u(3-t) = \int_{-\infty}^3 e^{-6t} = \infty$, therefore the system is not stable.

This system is neither causal or stable.

E

h(t) = $e^{-6|t|}$

Since h(t) $\neq$ 0 for t < 0 so the system is not causal.

$\int_{-\infty}^\infty e^{-6|t|} = 2\int_0^\infty e^{-6t} < \infty$. This system is stable.

This system is stable but not causal.

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