Revision as of 09:55, 21 November 2008 by Mcwalker (Talk | contribs)

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.

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang