Practice Scaling - 10.1.3.2 | 10. Fourier Cosine and Sine Transforms | Mathematics (Civil Engineering -1)
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Scaling

10.1.3.2 - Scaling

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

For the function f(x) = x^2 defined on [0, ∞), calculate the Fourier Cosine Transform.

💡 Hint: Remember to integrate by parts!

Challenge 2 Hard

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?

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