Practice Parseval’s Theorem for Fourier Transforms - 14.8 | 14. Parseval’s Theorem | Mathematics (Civil Engineering -1)
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14.8 - Parseval’s Theorem for Fourier Transforms

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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?

💡 Hint: Think about energy equivalence.

Question 2

Easy

Identify one condition for Parseval's theorem to be valid.

💡 Hint: Consider what is required for functions.

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 relate in signal analysis?

  • Total energy in time domain and frequency domain
  • Total amplitude in time domain and frequency domain
  • Total phase in time domain and frequency domain

💡 Hint: Think about what 'energy' means in terms of signals.

Question 2

True or False: Parseval's theorem is applicable only to periodic functions.

  • True
  • False

💡 Hint: Consider the broad applicability of the theorem.

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Challenge Problems

Push your limits with challenges.

Question 1

Given a non-periodic function f(t) = e^{-t} for t >= 0, verify Parseval's theorem by calculating its Fourier transform and showing the energy equivalence.

💡 Hint: Use the properties of the exponential function and perform the necessary integrals.

Question 2

In a structural analysis context, apply Parseval’s theorem to a complex wave signal composed of multiple sinusoidal components, verifying the total energy calculated matches between the signal's time domain and its frequency domain representation.

💡 Hint: Break down the complex wave into simpler sinusoidal functions.

Challenge and get performance evaluation