14.2 - Statement of Parseval’s Theorem
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Practice Questions
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What does Parseval’s Theorem relate in the context of a periodic function?
💡 Hint: Think about how energy is defined mathematically.
Define what a square integrable function is.
💡 Hint: Focus on the integral of the function squared.
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Interactive Quizzes
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What does Parseval’s Theorem equate in terms of a periodic function?
💡 Hint: Consider energy in both domains.
True or False: A function must be square integrable for Parseval’s Theorem to hold.
💡 Hint: Think about what it means for an integral to be finite.
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Challenge Problems
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A periodic function has Fourier coefficients a_0 = 2, a_1 = 3, and b_1 = 4. Using Parseval’s theorem, calculate the total energy over one period.
💡 Hint: Be careful with the coefficients you sum.
Show that for a square wave function with coefficients derived, Parseval's theorem holds true by calculating energy both ways (directly from f(x) and using coefficients).
💡 Hint: Refer to the properties of the square wave and its Fourier coefficients.
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