3015_Quiz_7_Solutions

# 3015_Quiz_7_Solutions - s-plane c There are poles lying in...

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University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Quiz #7 - Solutions Consider an LTI system with impulse response h ( t ) and system transfer function H ( s ) 1. If ) ( ) ( t u e t h t = , then the ROC of ) ( s H is: a) 0 } Re{ > s b) 1 } Re{ > s c) 1 } Re{ < s d) 1 } Re{ > s Sol: The system transfer function is given by ) 1 /( 1 ) ( + = s s H . The system has a pole at 1 = s . Because the signal is right-sided, the ROC is given by 1 } Re{ > s . 2. If ) ( s H is rational and the ROC of ) ( s H is 2 } Re{ < s , then: a) The system is stable and causal b) The system is unstable and causal c) The system is neither stable nor causal d) The system is stable and noncausal Sol: The ROC does not include the j ω -axis, hence the system is not stable. Furthermore, the ROC does not extend to the right of the right-most pole (wherever it is), so the system is not causal. 3. If the system is stable and causal, and if ) ( s H is rational, then: a) All the poles lie in the left-half of the s -plane b) All the poles lie in the right-half of the

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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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3015_Quiz_7_Solutions - s-plane c There are poles lying in...

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