Practice Orthogonal Functions: Concept And Properties (3.1) - Fourier Series Analysis of Continuous-Time Periodic Signals
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Orthogonal Functions: Concept and Properties

Practice - Orthogonal Functions: Concept and Properties

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define orthogonality in the context of functions.

💡 Hint: Think about the relationship between their inner product and overlap.

Question 2 Easy

What is an inner product for continuous functions?

💡 Hint: Remember the formula for the inner product!

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does it mean for two functions to be orthogonal?

They overlap entirely
Their inner product is zero
They can be represented as linear combinations

💡 Hint: Think about the inner product definition!

Question 2

True or False: sin(t) and cos(t) are orthogonal functions.

True
False

💡 Hint: Review the definition of the inner product.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the functions sin(kt), cos(kt) for different k are orthogonal over the interval [0, 2π].

💡 Hint: Utilize properties of integral and orthogonality.

Challenge 2 Hard

Show that any square-integrable function can be expressed using a complete orthogonal set.

💡 Hint: Consider the Fourier series representation.

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Reference links

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