10.1. Fourier Cosine Transform (FCT)

Try these first

1. 1.

   What is the formula for the Fourier Cosine Transform?

   Hint

   Look for the integral representation using cosine.

2. 2.

   State one application of the Fourier Cosine Transform.

   Hint

   Think of where these transforms help simplify conditions.

3. 3.

   What does the Fourier Cosine Transform do?

   • A. Converts frequency to time domain
   • B. Convert spatial function to frequency domain
   • C. Analyzes time-varying functions

   Hint

   Think about the domain shift involved.

4. 4.

   True or False: The FCT can only be applied to periodic functions.

   • True
   • False

   Hint

   Remember the definitions and where FCT is used.

5. 5.

   A function is given as f(x) = e^{-3x} for x >= 0. Compute its Fourier Cosine Transform.

   Hint

   Use the integral definition of the FCT.

6. 6.

   Discuss a scenario in civil engineering where FCT aids in decision making regarding structure design.

   Hint

   Think about structural responses to loads and how modulation helps.