15.4 - Limitations of Fourier Transforms
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Practice Questions
Test your understanding with targeted questions
What is the requirement for a function to be suitable for a Fourier transform?
💡 Hint: Think about integrals!
Define a causal system.
💡 Hint: Consider time relations!
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main limitation of the Fourier transform?
💡 Hint: Think about the properties of integrable functions.
True or False: Laplace transforms can handle functions that are not absolutely integrable over (-∞, ∞).
💡 Hint: Reflect on the time domains of these functions.
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Challenge Problems
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Develop a scenario where a Fourier transform fails to provide useful information due to the limitations. What would be a better approach?
💡 Hint: Think about systems responding to loads.
Explain how shifting from Fourier to Laplace transforms influences the analysis of civil engineering projects.
💡 Hint: Consider the importance of initial response analysis.
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