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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^{-3t}u(t)?
💡 Hint: Use the similar approach we applied to e^{-2t}.
Question 2
Easy
Describe the function represented by u(t).
💡 Hint: Think about its behavior for negative and positive values of t.
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 Fourier Transform of f(t) = e^{-2t}u(t)?
💡 Hint: Think about the general form of the Fourier Transform for exponential functions.
Question 2
Using the time-scaling property, what is F{rect(3t)}?
- (1/3)sinc(ω/3)
- (1/3)sinc(ω/6)
- (1/3)sinc(ω/9)
💡 Hint: Recall the effect of a time compression or expansion on the sinc function.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Explore the Fourier Transform of a combination function f(t) = e^{-t}u(t) + sin(t). How would you approach this?
💡 Hint: Break down the function into simpler parts before combining.
Question 2
Using f(t) = rect(t-1), determine how the Fourier Transform shifts in frequency domain.
💡 Hint: Consider the time-shifting property for insight into this shift.
Challenge and get performance evaluation