I'm trying to teach myself a bit of the content of signals and systems before the term starts using BP Lathi's "Linear Systems and Signals". I'm on convolutions now, and while I understand how to do them, I don't think I fully understand what exactly they are. 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-2tu(t) and x(t) = e-tu(t) The convolution x(t)*h(t) is e-t-e-2tu(t). 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. 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.