# Convolution problem

Hi i am really stuck trying to do this convolution in order to find zero state response. The convolution table only contains $(e^t)u(t)$ not $u(-t)$ can someone show me the steps with some brief explanation as well?

$x(t) * h(t)$

where

$x(t) = e^tu(-t)$

$h(t) = -\delta (t) + 2e^{-t} u(t)$

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What is $x(t)*h(t)$? Recall that $x(t)$ and $h(t)$ are numbers, not functions. – Did Oct 22 '11 at 16:50
I assume that this is homework since the question is typical of those asked in a first course on "Signals and Systems" in an electrical engineering curriculum. If so, please add the homework tag. I won't give you the answer but only a hint or two. I doubt very much that your convolution table has $e^tu(t)$ in it; it probably has $e^{−t}u(t)$. My recommendation is to draw a sketch of $e^{−t}u(t)$ and of the function $e^{t}u(-t)$ to see what the functions look like. Then, $$x(t)∗h(t) = -x(t)∗δ(t) + 2(e^{t}u(-t))∗(e^{−t}u(t))$$ where at least one convolution is probably in your table. – Dilip Sarwate Oct 23 '11 at 3:08