Practice Properties Of The Z-transform (4.4) - Time and Frequency Domains: Z-Transform
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Properties of the Z-Transform

Practice - Properties of the Z-Transform

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Z-Transform of a signal $x[n] = 2$?

💡 Hint: Think about how constant signals behave in Z-domain.

Question 2 Easy

Describe the linearity property of the Z-Transform.

💡 Hint: Think of combining two musical notes.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Z-Transform of $x[n] = n$?

$X(z) = z/(1 - z^{-1})^2$
$X(z) = 1/(1 - z)$
$X(z) = 1/(1 + z)$

💡 Hint: Think about the derivative of a geometric series.

Question 2

True or False: The Z-Transform of a right-sided signal has a ROC extending outward from the origin.

True
False

💡 Hint: Remember the characteristics of causal signals.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the signals $x[n] = 2^n u[n]$ and $h[n] = 3^n u[n]$, compute the Z-Transform and demonstrate the convolution in Z-domain.

💡 Hint: Focus on finding each Z-Transform first, then multiply.

Challenge 2 Hard

Apply the Final Value Theorem to find the steady-state value of the signal $x[n] = (0.5)^n u[n]$.

💡 Hint: Identify the Z-Transform first, then follow limits.

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Reference links

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