Practice Scaling (Time Scaling) - 3.3.5 | Module 3: Fourier Series Analysis of Continuous-Time Periodic Signals | Signals and Systems
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Academics

Grades

Grade 8 Grade 9 Grade 10 Grade 11 Grade 12

Curriculum

CBSE ICSE IB
Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Professional Courses
Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

games
Typing
Memory
Math
English Adventures
Knowledge

3.3.5 - Scaling (Time Scaling)

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What happens to the period of a signal when it is scaled by a factor of 2?

💡 Hint: Think about how scaling affects duration.

Question 2

Easy

How does scaling by a factor less than 1 affect the frequency?

💡 Hint: Remember, stretching means longer time to complete the cycle.

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 new fundamental period T_0' if the original period T_0 is scaled by a factor of alpha?

  • T_0 / alpha
  • alpha * T_0
  • T_0 + alpha

💡 Hint: Think about dividing the original period by the scaling factor.

Question 2

If the angular frequency is omega_0, what is the new angular frequency after scaling?

  • True
  • False

💡 Hint: Consider how scaling factors affect frequency.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

For a signal with a fundamental period of 6 seconds, if we time scale it by a factor of 3, what will be the new period and angular frequency? Also, determine the new association of its Fourier coefficients.

💡 Hint: Break down the problem into steps: first calculate the period, then the frequency, and lastly relate it to the coefficients.

Question 2

A signal with original frequencies and its Fourier coefficients c_k shows specific values. If time is scaled up by a factor of 0.5, how will the representation of these coefficients change?

💡 Hint: Focus on understanding how scaling alters frequency while coefficients maintain their values.

Challenge and get performance evaluation