I’m excited about this sequence! The rephrasing in terms of convolution is really helpful!
That being said, this is at least the tenth time that I see this animation of convoluting two box functions, and it is definitely the most confusing mathematical figure I’ve ever seen. Why is there 3 variables tracked by the x-axis?
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?)
I’m excited about this sequence! The rephrasing in terms of convolution is really helpful!
That being said, this is at least the tenth time that I see this animation of convoluting two box functions, and it is definitely the most confusing mathematical figure I’ve ever seen. Why is there 3 variables tracked by the x-axis?
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?)