11.6. Important Standard Fourier Transforms

Try these first

1. 1.

   What is the Fourier Transform of the Dirac delta function?

   Hint

   Think about the property of impulse signals.

2. 2.

   What is the Fourier Transform of e^(-at)u(t)?

   Hint

   Consider what happens to exponential decay in the frequency space.

3. 3.

   What is the Fourier Transform of δ(t)?

   • 1
   • 2πδ(ω)
   • 0

   Hint

   Consider impulse response.

4. 4.

   True or false: The Fourier Transform of e^(-at)u(t) is 1/(a+iω).

   • True
   • False

   Hint

   Think about the behavior of decaying signals.

5. 5.

   Find the Fourier Transform of a signal composed of both sin(2t) and cos(2t).

   Hint

   Use linearity of transforms.

6. 6.

   Derive the Fourier Transform for a piecewise rectangular function.

   Hint

   Break it into manageable segments.