Practice Complex Form of Fourier Integral - 9.9 | 9. Fourier Integrals | Mathematics (Civil Engineering -1)
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9.9 - Complex Form of Fourier Integral

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define the complex Fourier integral.

💡 Hint: Recall how this integrates over the entire real line.

Question 2

Easy

What is the Fourier transform?

💡 Hint: It transforms a time-domain function to the frequency domain.

Practice 3 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 is the key representation of complex Fourier integrals?

  • $$f(x) = \\int fb(\\omega)e^{i\\omega x}d\\omega$$
  • $$f(x) = \\frac{1}{2\\pi}\\int fb(\\omega)e^{i\\omega x}d\\omega$$
  • $$f(x) = \\int fb(\\omega)e^{-i\\omega x}d\\omega$$

💡 Hint: Consider the factors included in the representation.

Question 2

True or False: The Fourier transform can only be used for periodic functions.

  • True
  • False

💡 Hint: Remember the criteria for using Fourier transforms.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Demonstrate the use of complex Fourier integrals by transforming a non-periodic function, such as a Gaussian, and explain the significance in practical terms.

💡 Hint: Consider properties of exponential functions and integrals with Gaussian forms.

Question 2

Evaluate how the complex form simplifies the solution of a differential equation related to a heat transfer problem.

💡 Hint: Look for how combining terms into exponentials reduces the complexity of boundary condition applications.

Challenge and get performance evaluation