Can someone explain the convolusion integral to me?

Ok, to start this off I understand WHAT convolution does. I know what its visual representation is. I can convolve using graphical techniques.

For some reason, even after 3 classes where we touched on convolution, I do not understand how to do the convolution integral. I want to know how to perform the convolution integral using 2 time functions and come up with a function that represents the resulting waveform/function.

So if I want to, for example, convolve 3cos(120t) with 5sin(80t) and come up with and equation the represents the convolution of those functions how do I do it? I know this is elementary to most EE’s, but it is just not clicking with me for some reason.

The definition of the convolution of g(x) and h(x) is the integral from -infinity to infinity of g(z)h(x - z)dz. “z” is a dummy variable that gets integrated out. Which of your functions you make “g” or “h” doesn’t matter.

For your example, integrate 15cos(120z)sin(80t - z)dz from -infinity to infinity.