13.1.5.3. Distributive over addition

Try these first

1. 1.

   Define convolution in your own words.

   Hint

   Think about how two signals can influence one another over time.

2. 2.

   What does the distributive property of convolution state?

   Hint

   Consider the parts involved in the convolution and how they can be simplified.

3. 3.

   What is the definition of convolution?

   Hint

   Think of how two signals interact over time.

4. 4.

   Does convolution distribute over addition?

   • True
   • False

   Hint

   Recall the formula for the distributive property.

5. 5.

   Given $f(t) = t$ and $g(t) = e^{-t}$, compute $(f * g)(t)$ and verify the result using the Distributive Property.

   Hint

   Before integrating, think about parts you can simplify.

6. 6.

   Show that the output of a system described by the Laplace transform $F(s) \cdot G(s)$ is equivalent to the convolution in time domain of the functions $f(t)$ and $g(t)$.

   Hint

   Break down each transformation to reveal the convolution aspect clearly.