12.3.2. Convolution Theorem

Try these first

1. 1.

   What is the Convolution Theorem?

   Hint

   Think about how functions combine over time.

2. 2.

   List the components in the integral used in the Convolution Theorem.

   Hint

   Focus on understanding how each part contributes.

3. 3.

   What is the formula for the convolution integral?

   Hint

   Reflect on the integral components.

4. 4.

   True or False: The Convolution Theorem is used for the addition of two functions.

   Hint

   Remember the core operations involved.

5. 5.

   Given two functions f₁(t) = e^{-2t} and f₂(t) = t^2, use the Convolution Theorem to find their convolution. Detail each step you take.

   Hint

   Break the integrals into manageable parts.

6. 6.

   A control system is defined by the product of two Laplace transforms. Describe the process you would take to find the output in the time domain.

   Hint

   Focus on the influence of each part individually.