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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the Fourier Transform of f(t) = e^{-2t}u(t)?
💡 Hint: Use the transformation formula and evaluate the integral.
Question 2
Easy
Define the unit step function.
💡 Hint: Think about the switching behavior of the function.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the general form of the Fourier Transform?
- ∫ f(t)e^{-iωt} dt
- ∫ e^{at} dt
- f(t) + g(t)
💡 Hint: Recall the formula we discussed during the lecture.
Question 2
True or False: The Fourier Transform of e^{-at}u(t) results in a complex function.
- True
- False
💡 Hint: Think about how imaginary units appear in the transformation.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(t) = e^{-2t}u(t), derive the Fourier Transform and explain how it can be used in practical applications such as signal processing.
💡 Hint: Use the steps of integration and pay attention to how limits affect your result.
Question 2
Explore the implications of changing 'a' in the function f(t) = e^{-at}u(t) on the resultant Fourier Transform. Discuss at least two scenarios.
💡 Hint: Consider values of 'a' such as 1, 2, and how it affects the transform's output.
Challenge and get performance evaluation