(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Compute the following

[tex]y(t)=e^{-3t}u(t)\ast u(t+3)[/tex]

2. Relevant equations

u(t) is the unit step function.

3. The attempt at a solution

I get confused with these for some reason...

[tex]y(t)= \int^{+\infty}_{-\infty}e^{-3 \tau}u(\tau)u(t-\tau+3)d\tau[/tex]

This is where I have my first problem, trying to eliminate the step functions. I tried

[tex]y(t)= \int^{t+3}_{0}e^{-3 \tau}d\tau[/tex]

Does that look right?

Finally integrating that with my limits gave:

[tex][1/3 - e^{-3(t+3)}]u(t+3)[/tex]

Now the step function I added at the end, and I'm not quite sure why... My main problem is dealing with the step functions, any suggestions/ confirmations I did it wrong or right?

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# Homework Help: Convolution Integrals

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