Midterm_solution

Midterm_solution - Midterm Solution Solution by Harvey...

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Unformatted text preview: Midterm Solution Solution by Harvey Thornburg 1. (a) Factor H ( s ) = s +4 ( s +1)( s +2) . There are two poles : s =- 1 and s =- 2, and only one zero : s =- 4. (b) Possible ROC is: Re { s } >- 1- 2 < Re { s } <- 1 Re { s } <- 2 As Re { s } >- 1 contains the j-axis, the system is stable. (c) As Re { s } >- 1 is right-sided, the system is causal. (d) H- 1 ( s ) = ( s +1)( s +2) s +4 It seems that H- 1 ( s ), with ROC: Re { s } >- 4, does work here. However, there is an important subtlety that some of you mentioned. Since the degree of numerator is larger than the degree of the denom- inator, we can write: H- 1 ( s ) = s 2 + 3 s + 2 s + 4 = s- s- 2 s + 4 (1) Lets consider the system H ( s ) = s . It is a differentiator, and is differentiation BIBO stable? Consider x ( t ) = sin t 2 bounded x ( t ) = 2 t cos t 2 unbounded So, having all poles in left-half plane does not, on its own, guarantee BIBO stability....
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Midterm_solution - Midterm Solution Solution by Harvey...

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