Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skillsβperfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define orthogonal functions in your own words.
π‘ Hint: Consider the definition involving their inner product.
Question 2
Easy
What is the formula for calculating the norm of a function?
π‘ Hint: Recall the relationship between inner products and norms.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the inner product of two orthogonal functions?
- True
- False
π‘ 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.
π‘ Hint: Think about the definition of an orthonormal set.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Demonstrate orthogonality between the functions f(t) = sin(t) and g(t) = cos(t) over the interval [0, 2Ο]. Calculate their inner product.
π‘ Hint: Use integration by parts or the identity of sin and cos.
Question 2
Discuss how the concepts of orthogonality and orthonormality can be applied in signal processing to optimize filter design.
π‘ Hint: Think about how coefficients are summed in signal processing.
Challenge and get performance evaluation