Practice Time Scaling (11.3.4) - Fourier Transform and Properties - Mathematics (Civil Engineering -1)

Practice: Time Scaling

Lesson 11.3.4Fourier Transform and Properties

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8 questions

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6 sample questions

Question 1.
What happens to a function when it is scaled in time by a factor of 2?
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Remember how speed affects time duration.
Question 2.
Write the formula for the Fourier Transform of a time-scaled function.
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Think about how the scaling factor appears in the equation.
3Question 3.
What is the effect of scaling a function in time?
- Affects the amplitude only
- Changes the frequency representation
- Has no effect
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Think about how speeding up a signal affects its tone.
4Question 4.
Time scaling contracts the signal in the time domain and what occurs to the frequencies?
- True
- False
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Consider how shorter durations relate to higher pitches.
Question 5.
Let f(t) = sin(t). Apply a time scaling of 'a=3/2'. Derive the new Fourier Transform.
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Focus on multiplying with the scaling factor.
Question 6.
In a civil engineering context, analyze how a time-scaling adjustment for response data in a seismic event could change interpretation of results.
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Think about the implications of observing quicker oscillations.

4 more questions in this section. Enroll free to practise them all.