11.3.4. Time Scaling

Try these first

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.