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11.3.4. Time Scaling

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  1. 1.

    What happens to a function when it is scaled in time by a factor of 2?

    Hint

    Remember how speed affects time duration.

  2. 2.

    Write the formula for the Fourier Transform of a time-scaled function.

    Hint

    Think about how the scaling factor appears in the equation.

  3. 3.

    What is the effect of scaling a function in time?

    • Affects the amplitude only
    • Changes the frequency representation
    • Has no effect
    Hint

    Think about how speeding up a signal affects its tone.

  4. 4.

    Time scaling contracts the signal in the time domain and what occurs to the frequencies?

    • True
    • False
    Hint

    Consider how shorter durations relate to higher pitches.

  5. 5.

    Let f(t) = sin(t). Apply a time scaling of 'a=3/2'. Derive the new Fourier Transform.

    Hint

    Focus on multiplying with the scaling factor.

  6. 6.

    In a civil engineering context, analyze how a time-scaling adjustment for response data in a seismic event could change interpretation of results.

    Hint

    Think about the implications of observing quicker oscillations.

Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Quiz

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Challenge Problems

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting