m (2.29 (a,b,e) moved to 2.29 (a,b,e) (ECE301Summer2008asan)) 

(No difference)

Revision as of 11:07, 21 November 2008
Find if each system is stable and causal.
A
h(t) = $ e^{4t} u(t2) $
u(t2) = 1 for t >= 2 making h(t) = 0 for t < 2. The system is causal.
$ \int_{\infty}^\infty e^{4t} u(t2) = /int_2^\infty e^{4t} < \infty $. Therefore the system is stable.
This system is stable and causal.
B
h(t) = $ e^{6t} u(3t) $
u(3t) = 1 for t<=3, making h(t) $ \neq $ for t < 0. The system is not causal.
$ \int_{\infty}^\infty e^{6t} u(3t) = \int_{\infty}^3 e^{6t} = \infty $, therefore the system is not stable.
This system is neither causal or stable.
E
h(t) = $ e^{6t} $
Since h(t) $ \neq $ 0 for t < 0 so the system is not causal.
$ \int_{\infty}^\infty e^{6t} = 2\int_0^\infty e^{6t} < \infty $. This system is stable.
This system is stable but not causal.