Practice - Properties of Orthogonal and Orthonormal Functions
Practice Questions
Test your understanding with targeted questions
Define orthogonal functions in your own words.
💡 Hint: Consider the definition involving their inner product.
What is the formula for calculating the norm of a function?
💡 Hint: Recall the relationship between inner products and norms.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the inner product of two orthogonal functions?
💡 Hint: Recall the definition of orthogonality.
Which of the following defines a unit norm?
💡 Hint: Think about the definition of an orthonormal set.
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Challenge Problems
Push your limits with advanced challenges
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.
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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Reference links
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