Practice - Region of Convergence (ROC) and its Definitive Properties
Practice Questions
Test your understanding with targeted questions
What does ROC stand for?
💡 Hint: Think about what part of the Laplace Transform it relates to.
Why can't the ROC contain poles of X(s)?
💡 Hint: Consider what happens to the integral at those points.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the ROC verify in terms of Laplace Transform?
💡 Hint: Think about the purpose of the ROC.
True or False: A system is causal if its ROC includes the imaginary axis.
💡 Hint: Consider the definitions of causality.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given X(s) = (s+2)/(s^2 + 4s + 5), determine the ROC and characterize the system's stability.
💡 Hint: Factor the denominator to identify poles.
For the function x(t) = e^(2t)u(t), find its Laplace Transform and ROC, then discuss the implications for stability.
💡 Hint: Evaluate the implications of the pole's location.
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