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So, for a given unit impulse response h(t) and an input x(t), the response y(t) is the convolution of x(t) with h(t). For example (going off of what was in the book), if

*h(t) = e*

^{-2t}u(t)and

*x(t) = e*

^{-t}u(t)The convolution x(t)*h(t) is

*e*. The other convolution drills I was able to solve without trouble. However, I don't feel like I understand intuitively what convoluting two signals is actually doing.

^{-t}-e^{-2t}u(t)Furthermore, I don't get what the connection is to the Laplace transform, which was touched on very briefly in my introductory differential equations course but not really explained. I understood how to use convolutions with Laplace transform problems, but still, I don't philosophically understand what's happening.