View source for 2.28 (a,b,c) (ECE301Summer2008asan) - Rhea

[[Category:ECE301Summer08asan]]
[[Category: ECE]]
[[Category: ECE 301]]
[[Category: Summer]]
[[Category: 2008]]
[[Category: asan]]
[[Category: Homework]]
=Problem 2.28, [[Homework_3_-_Summer_08_%28ECE301Summer2008asan%29|HW3]], [[ECE301]], Summer 2008=
Determine if each system is causal and stable.

'''A'''

h[n] = (1/5)<math>^n</math> u[n]

For n < 0 h[n] = 0 therefore h[n] is causal.

<math>\Sigma_{n=0}^\infty</math> (1/5)<math>^n</math> < <math>\infty</math> since lim<math>_{n->\infty}</math> = 0

The system is both causal and stable.

'''B'''

h[n] = <math>(0.8)^n</math> u[n+2]

Since u[n+2] = 1 for n >= -2 and 0 for n < -2 the system is not causal because h[n] <math>\neq</math> 0 for t < 0.

<math>\Sigma_{n = -2}^\infty</math> <math>(0.8)^n</math> < <math>\infty</math> since <math>lim_{n->\infty} (0.8)^n = 0</math>, the system is stable.

The system is not causal and stable.

'''D'''

h[n] = 5<math>^n</math>u[3-n]

Since u[3-n] = 1 for n <= 3 and 0 for n > 3, h[n] <math>\neq</math> 0 for t < 0.

<math>\Sigma_{-\infty}^\infty 5^n u[3-n] = \Sigma_{-\infty}^3 5^n < \infty</math>, therefore the system is stable.

This system is stable but not causal.
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