Practice Initial And Final Value Theorems (4.4.5) - Time and Frequency Domains: Z-Transform
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Initial and Final Value Theorems

Practice - Initial and Final Value Theorems

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the Initial Value Theorem help us find?

💡 Hint: Think about the value of the signal at n=0.

Question 2 Easy

State the formula for the Final Value Theorem.

💡 Hint: Remember this links the Z-domain and long-term behavior.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Initial Value Theorem state?

It finds the initial value from X(z) as z approaches 0.
It finds the initial value from X(z) as z approaches ∞.
It determines stability of a system.
It calculates the area under the curve.

💡 Hint: Remember 'I For Infinity'.

Question 2

True or false: The Final Value Theorem can predict if a signal diverges.

True
False

💡 Hint: Consider what happens to a signal over time.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the Z-Transform X(z) = (3z/(z^2 - z - 6)), determine if the signal is stable and find initial and final values.

💡 Hint: Analyze the poles to determine stability and apply the tests for initial and final values separately.

Challenge 2 Hard

A system has the Z-Transform X(z) = (2z^2)/(z^2 + 4z + 4). Calculate the initial and final values, and discuss system stability.

💡 Hint: Evaluate the roots of the denominator for stability and apply the theorems.

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Reference links

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