Practice Orthogonal Sets And Complete Sets Of Functions (3.1.2) - Fourier Series Analysis of Continuous-Time Periodic Signals
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Orthogonal Sets and Complete Sets of Functions

Practice - Orthogonal Sets and Complete Sets of Functions

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define 'orthogonal set' in your own words.

💡 Hint: Think about functions that do not overlap.

Question 2 Easy

What is the inner product of two functions?

💡 Hint: Consider it as measuring how similar or different two functions are.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What defines an orthogonal set of functions?

A collection where all functions are equal.
A collection where any two functions integrate to zero.
A collection with infinite elements.

💡 Hint: Think about integration results over specific intervals.

Question 2

True or False: A complete set of functions can represent every possible function.

True
False

💡 Hint: Consider 'well-behaved' functions.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given two functions sin(t) and cos(t), calculate their inner product over the interval [0, 2π]. What conclusion can you draw?

💡 Hint: Set up the integral and apply the orthogonality condition.

Challenge 2 Hard

Demonstrate how to represent a non-square-integrable function using an incomplete set of Fourier series terms.

💡 Hint: Consider practical examples where harmonics are missed.

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Reference links

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