11.7.1. Fourier Transform of Rectangular Pulse

Try these first

1. 1.

   Define a rectangular pulse function.

   Hint

   Think about how you would draw it.

2. 2.

   What is the Fourier Transform of a rectangular pulse?

   Hint

   Recall the definition of the sinc function.

3. 3.

   What is the value of f(t) for |t| ≤ T/2 in a rectangular pulse?

   • 0
   • 1
   • T

   Hint

   Consider the definition of the pulse.

4. 4.

   Is the Fourier Transform of a rectangular pulse a sinc function?

   • True
   • False

   Hint

   Recall the transformation results.

5. 5.

   A rectangular pulse of width T is shifted in time. What impact does this have on its Fourier Transform?

   Hint

   Recall the time-shifting property of Fourier transforms.

6. 6.

   How would the Fourier Transform change if the pulse width T is doubled?

   Hint

   Consider how time compression affects frequency expansion.