Chapter 15, Problem 46P

Given the following functions

$x\left(t\right)=2\delta \left(t\right),y\left(t\right)=4u\left(t\right),z\left(t\right)=e^{-2t}u\left(t\right),$

evaluate the following convolution operations.

1. (a) $x\left(t\right)*y\left(t\right)$
2. (b) $x\left(t\right)*z\left(t\right)$
3. (c) $y\left(t\right)*z\left(t\right)$
4. (d) $y\left(t\right)*\left[y\left(t\right)+z\left(t\right)\right]$