10.1.1 - Definition
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Practice Questions
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What is the definition of the Fourier Cosine Transform?
💡 Hint: Think about how this transform relates to frequency.
What is the inverse Fourier Cosine Transform used for?
💡 Hint: What operation helps us revert to the original function?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Fourier Cosine Transform decompose?
💡 Hint: Think about the type of basis functions used.
True or False: The inverse Fourier Cosine Transform is used to return to the spatial domain.
💡 Hint: Consider what transforms lead to the original function.
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Challenge Problems
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Calculate the Fourier Cosine Transform of the function $$ f(x) = x^2 $$ over [0, ∞).
💡 Hint: Consider integration by parts for this problem.
Examine the effects of changing parameters in the FCT with different exponential functions. What does it tell you about behavior in the frequency domain?
💡 Hint: Analyze how the decay rate affects the amplitude in the frequency domain.
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