Practice - Scaling in the Z-Domain
Practice Questions
Test your understanding with targeted questions
What is the new Z-Transform when a signal x[n] = 5^n is scaled by a factor of 2?
💡 Hint: Apply the scaling property with the Z-Transform.
If x[n] has a Z-Transform of X(z), what will the Z-Transform be for a[n] = 3^n x[n]?
💡 Hint: Remember the scaling rule.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does scaling a discrete-time signal x[n] by a^n do to its Z-Transform?
💡 Hint: Think about how the Z-Transform is defined with respect to scales.
Scaling a signal can affect its stability. True or False?
💡 Hint: Refer back to how ROC is impacted by signal scaling.
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Challenge Problems
Push your limits with advanced challenges
Suppose x[n] = 3^n * u[n]. Find its Z-Transform and explain the stability of the system based on the ROC.
💡 Hint: Determine the ROC based on the signal’s growth.
Given the signal y[n] = 0.5^n * u[n], determine the Z-Transform after scaling by a factor of 4.
💡 Hint: Analyze the output response concerning the scaled Z-Transform.
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Reference links
Supplementary resources to enhance your learning experience.