11.2 - Conditions for Existence (Dirichlet’s Conditions)
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Practice Questions
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What does it mean for a function to be absolutely integrable?
💡 Hint: Think about the convergence of the integral.
What is one example of a condition for function existence?
💡 Hint: Consider the behavior of discontinuities.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which of the following is a condition for the existence of a Fourier Transform?
💡 Hint: Recall the integral criteria.
True or False: A function can have an infinite number of maxima and still have a Fourier Transform.
💡 Hint: Think about the conditions we discussed.
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Challenge Problems
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Consider the function f(t) = 1/t for t > 1 and 0 for t <= 1. Analyze whether this function meets Dirichlet's Conditions.
💡 Hint: Evaluate both endpoints of the function interval.
Given f(t) = cos(t^2), describe whether it meets Dirichlet’s Conditions within the interval [-T, T].
💡 Hint: Assess the frequency of oscillation and consider integration over the range.
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