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Unformatted text preview: splane c) There are poles lying in both the lefthalf and the righthalf of the splane d) ) ( s H cannot have any pole Sol: If the system is stable, the ROC must include the j ωaxis. Moreover, if the system is causal, the ROC must be to the right of the rightmost pole. Hence, the system can only be both stable and causal simultaneously if ALL poles lie in the lefthalf of the plane. 4. If the ROC of ) ( s H expands the entire splane, then the system is: a) unstable b) stable but not necessarily causal c) stable and causal d) unstable and noncausal Sol: If the ROC expands the entire splane, it includes the j ωaxis, and thus the system is stable. However, causality may not be guaranteed. For example, a system with impulse response ) 1 ( ) 1 ( ) ( − − + = t u t u t h has a Laplace Transform that expands the entire splane, yet is not causal....
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 Fall '08
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 LTI system theory

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