# Convolution with rectangular function

I have a system $$h(t)=4e^{-4(t-4)}u(t-4)$$ and I want to response of the system to $$x(t)=rect(2(t+4))$$. I have followed those steps:

$$y(t)=x(t){*}h(t)$$

$$=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$$

$$=4[u(t)-u(t+8)] { * } e^{-4(t-4)}u(t-4)$$

$$=4[u(t){*}e^{-4(t-4)}u(t-4)] - 4[u(t+8){*}e^{-4(t-4)}u(t-4)]$$

I got stuck after this point. I have an exam in a week. Thanks in advance for the help.

• Now it's time to actually calculate the necessary convolutions by using the definition of convolution for continuous-time signals. What keeps you from doing just that? – Matt L. Dec 26 '18 at 13:15