Practice Statement of Parseval’s Theorem - 14.2 | 14. Parseval’s Theorem | Mathematics (Civil Engineering -1)
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14.2 - Statement of Parseval’s Theorem

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does Parseval’s Theorem relate in the context of a periodic function?

💡 Hint: Think about how energy is defined mathematically.

Question 2

Easy

Define what a square integrable function is.

💡 Hint: Focus on the integral of the function squared.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does Parseval’s Theorem equate in terms of a periodic function?

  • A) The function's value at a specific point.
  • B) The total energy in time domain and the sum of squares of Fourier coefficients.
  • C) The rate of change of the function.

💡 Hint: Consider energy in both domains.

Question 2

True or False: A function must be square integrable for Parseval’s Theorem to hold.

  • True
  • False

💡 Hint: Think about what it means for an integral to be finite.

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Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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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