13.1.1. Introduction

Try these first

1. 1.

   Define convolution in your own words.

   Hint

   Think about how two functions can interact over time.

2. 2.

   List the three properties of convolution.

   Hint

   Remember the acronym CAD!

3. 3.

   What does the Convolution Theorem simplify?

   • Finding the limit of a function
   • Inverse Laplace Transform of product functions
   • Derivative of functions

   Hint

   Think about what the theorem aims to achieve!

4. 4.

   True or False: The convolution of f(t) and g(t) is the same as g(t) and f(t).

   • True
   • False

   Hint

   Refer back to the properties of convolution.

5. 5.

   Derive the inverse Laplace transform of the product of functions f(t) = e^(-3t) and g(t) = sin(2t) using the Convolution Theorem.

   Hint

   Remember to think about how the functions overlap as one shifts over the other.

6. 6.

   Explore a real-world scenario where understanding convolution could influence design choices in a control system.

   Hint

   Consider system feedback loops and delays.