Practice Properties Of Orthogonal And Orthonormal Functions (3.1.3) - Fourier Series Analysis of Continuous-Time Periodic Signals
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Properties of Orthogonal and Orthonormal Functions

Practice - Properties of Orthogonal and Orthonormal Functions

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Practice Questions

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Question 1 Easy

Define orthogonal functions in your own words.

💡 Hint: Consider the definition involving their inner product.

Question 2 Easy

What is the formula for calculating the norm of a function?

💡 Hint: Recall the relationship between inner products and norms.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the inner product of two orthogonal functions?

True
False

💡 Hint: Recall the definition of orthogonality.

Question 2

Which of the following defines a unit norm?

The norm is less than one.
The norm is exactly one.
The norm can be any positive value.

💡 Hint: Think about the definition of an orthonormal set.

1 more question available

Challenge Problems

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Challenge 1 Hard

Demonstrate orthogonality between the functions f(t) = sin(t) and g(t) = cos(t) over the interval [0, 2π]. Calculate their inner product.

💡 Hint: Use integration by parts or the identity of sin and cos.

Challenge 2 Hard

Discuss how the concepts of orthogonality and orthonormality can be applied in signal processing to optimize filter design.

💡 Hint: Think about how coefficients are summed in signal processing.

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