m (2.28 (a,b,c) moved to 2.28 (a,b,c) (ECE301Summer2008asan)) 

(No difference)

Revision as of 11:07, 21 November 2008
Determine if each system is causal and stable.
A
h[n] = (1/5)$ ^n $ u[n]
For n < 0 h[n] = 0 therefore h[n] is causal.
$ \Sigma_{n=0}^\infty $ (1/5)$ ^n $ < $ \infty $ since lim$ _{n>\infty} $ = 0
The system is both causal and stable.
B
h[n] = $ (0.8)^n $ u[n+2]
Since u[n+2] = 1 for n >= 2 and 0 for n < 2 the system is not causal because h[n] $ \neq $ 0 for t < 0.
$ \Sigma_{n = 2}^\infty $ $ (0.8)^n $ < $ \infty $ since $ lim_{n>\infty} (0.8)^n = 0 $, the system is stable.
The system is not causal and stable.
D
h[n] = 5$ ^n $u[3n]
Since u[3n] = 1 for n <= 3 and 0 for n > 3, h[n] $ \neq $ 0 for t < 0.
$ \Sigma_{\infty}^\infty 5^n u[3n] = \Sigma_{\infty}^3 5^n < \infty $, therefore the system is stable.
This system is stable but not causal.