Practice Scaling (time Scaling) (3.3.5) - Fourier Series Analysis of Continuous-Time Periodic Signals
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Scaling (Time Scaling)

Practice - Scaling (Time Scaling)

Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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