11.7.2 - Fourier Transform of Exponential Decay
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Practice Questions
Test your understanding with targeted questions
What is the Fourier Transform of f(t) = e^{-2t}u(t)?
💡 Hint: Use the transformation formula and evaluate the integral.
Define the unit step function.
💡 Hint: Think about the switching behavior of the function.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the general form of the Fourier Transform?
💡 Hint: Recall the formula we discussed during the lecture.
True or False: The Fourier Transform of e^{-at}u(t) results in a complex function.
💡 Hint: Think about how imaginary units appear in the transformation.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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