15.3.2. Fourier Sine Transform (FST)

Try these first

1. 1.

   What is the mathematical expression for the Fourier Sine Transform?

   Hint

   Recall the integration limits for the sine-transform.

2. 2.

   What type of functions does the Fourier Sine Transform primarily work with?

   Hint

   Consider what 'piecewise' means in terms of function behavior.

3. 3.

   What is the definition of the Fourier Sine Transform?

   • A method to convert a time function into a frequency function using sine functions
   • A method to convert a time function into a frequency function using cosine functions
   • A graphical representation of functions over a finite interval

   Hint

   Focus on the function's behavior in relation to sine.

4. 4.

   Is the Fourier Sine Transform useful only for periodic functions?

   • True
   • False

   Hint

   Consider the definition's focus on non-periodic functions.

5. 5.

   Using the Fourier Sine Transform, compute the transformed integral for f(x) = x over the interval [0,∞].

   Hint

   Consider using integration by parts, where u = x and dv = sin(ωx) dx.

6. 6.

   Given a function f(x) = e^(-ax) for x >= 0, compute its Fourier Sine Transform.

   Hint

   The integral can be solved using a standard table of integrals or through integration by parts.