11.1. Definition of Fourier Transform

Try these first

1. 1.

   What is the Fourier Transform used for?

   Hint

   Think about signal processing.

2. 2.

   What do we call the function F(ω) produced by the Fourier Transform?

   Hint

   What domain does F(ω) represent?

3. 3.

   What does the Fourier Transform convert?

   • Time-domain to frequency-domain
   • Frequency-domain to time-domain
   • Spatial to time-domain

   Hint

   Think of what happens to the signal in Fourier analysis.

4. 4.

   True or False: The Inverse Fourier Transform is used to recover the original time signal.

   • True
   • False

   Hint

   It's the reverse of Fourier Transform.

5. 5.

   Consider a function f(t) = cos(2t) + sin(3t). Calculate its Fourier Transform.

   Hint

   Decompose into sine and cosine terms for easier transformation.

6. 6.

   Explain the significance of the Fourier Transform in signal processing with an example.

   Hint

   Think about the roles of frequency in both signals.