Ha—after I put the animated graphs in I was thinking, “maybe everyone’s already seen these a bunch of times...”.
As for the three functions all being plotted on the same graph: this is a compact way of showing three functions: f, g, and f * g. You can imagine taking more vertical space, and plotting the blue line f in one plot by itself—then the red line g on its own plot underneath—and finally the black convolution f * g on a third plot. They’ve just been all laid on top of each other here to fit everything into one plot. In my next post I’ll actually have the more explicit split-out-into-three-plots design instead of the overlaid design used here. (Is this what you meant?)
Ha—after I put the animated graphs in I was thinking, “maybe everyone’s already seen these a bunch of times...”.
As for the three functions all being plotted on the same graph: this is a compact way of showing three functions: f, g, and f * g. You can imagine taking more vertical space, and plotting the blue line f in one plot by itself—then the red line g on its own plot underneath—and finally the black convolution f * g on a third plot. They’ve just been all laid on top of each other here to fit everything into one plot. In my next post I’ll actually have the more explicit split-out-into-three-plots design instead of the overlaid design used here. (Is this what you meant?)