Practice Example Problems (11.8) - Fourier Transform and Properties - Mathematics (Civil Engineering -1)
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Example Problems

Practice - Example Problems

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Practice Questions

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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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

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Challenge 1 Hard

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.

Challenge 2 Hard

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.

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