Practice Unit Step Function (u(t)) (4.4.3) - Fourier Transform Analysis of Continuous-Time Aperiodic Signals
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Unit Step Function (u(t))

Practice - Unit Step Function (u(t))

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define the Unit Step Function, u(t).

💡 Hint: Think of it as a switch that turns on at t = 0.

Question 2 Easy

What does the Fourier Transform of a unit step function consist of?

💡 Hint: Consider the frequency components generated by the step change.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the definition of the Unit Step Function, u(t)?

0 for t < 0
1 for t >= 0
1 for t < 0
0 for t >= 0
only 0

💡 Hint: Remember how it behaves at t=0.

Question 2

The Fourier Transform of the Unit Step Function includes which of the following?

1/(jω)
1
e^(-jωt)

💡 Hint: Think about the relationship between the step and frequency responses.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a piecewise function representing a system where u(t) controls input, derive the output using F{u(t)}.

💡 Hint: Apply definitions from your learning on transforms with properties you derived.

Challenge 2 Hard

Explore how changing the step function to u(t - T) influences its Fourier Transform. What happens to its frequency representation?

💡 Hint: Consider how time shifts affect frequency representations in your study.

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Reference links

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