Practice Z-transform And Stability (4.5) - Time and Frequency Domains: Z-Transform
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Z-Transform and Stability

Practice - Z-Transform and Stability

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define stability in the context of discrete-time systems.

💡 Hint: Consider what happens to the output when the input is constant.

Question 2 Easy

What is the Z-transform?

💡 Hint: Think of how we convert signals into a different domain.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What indicates a stable discrete-time system?

A) The ROC does not include |z|=1
B) The ROC includes |z|=1
C) The ROC is infinite

💡 Hint: Consider the definition of stability tied to ROC.

Question 2

True or False: Anti-causal systems can be stable if the ROC is inward from the origin.

True
False

💡 Hint: Recall the characteristics of anti-causal systems.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a system with the Z-transform X(z) = 1/(1-0.5z^-1). Analyze its stability.

💡 Hint: Determine where the pole lies in relation to |z|=1.

Challenge 2 Hard

If a two-sided system has the ROC between |z|=0.5 and |z|=2, is it stable? Explain.

💡 Hint: Analyze the necessary conditions for stability regarding the ROC.

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Reference links

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