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Unformatted text preview: s-plane c) There are poles lying in both the left-half and the right-half of the s-plane d) ) ( s H cannot have any pole Sol: If the system is stable, the ROC must include the j ω-axis. Moreover, if the system is causal, the ROC must be to the right of the right-most pole. Hence, the system can only be both stable and causal simultaneously if ALL poles lie in the left-half of the plane. 4. If the ROC of ) ( s H expands the entire s-plane, 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 s-plane, it includes the j ω-axis, 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 s-plane, yet is not causal....
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- Fall '08