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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the definition of Fourier Cosine Transform?
💡 Hint: Review the definition in your notes.
Question 2
Easy
State the linearity property of FCT.
💡 Hint: Think about how we can combine two 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 is the formula for the Fourier Cosine Transform?
- F(s) = \\int f(x) \\cos(sx) dx
- F(s) = \\frac{2}{\\pi} \\int_{0}^{\\infty} f(x) \\cos(sx) dx
- F(s) = \\int_{0}^{\\infty} f(x) \\sin(sx) dx
💡 Hint: Look for the integral limits and constants.
Question 2
True or False: The scaling property of the Fourier Cosine Transform states that F{f(ax)} = aF{f(x)}.
- True
- False
💡 Hint: Recall the specific coefficients involved in scaling.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
For the function f(x) = x^2 defined on [0, ∞), calculate the Fourier Cosine Transform.
💡 Hint: Remember to integrate by parts!
Question 2
Discuss how the Parseval's Identity can be applied in a physical context, such as sound waves.
💡 Hint: What does energy conservation mean in this context?
Challenge and get performance evaluation