The convolution

This is a visual approach showing how the convolution operation works.

First observe how a system (i.e.a copper line) transforms an input pulse into an (here adjustable) spread shape.

The input pulse is on the right, and the output is given on the left (between the two vertical lines).

Now, since the system is characterized by its answer h(t) to an input pulse, the output (answser) s(t) to any input e(t) can be computed: s(t)=the convolution product of the input signal (e(t) and the the specific answser h(t) to a pulse.
Draw with mouse (click on right grey zone) an input signal as a sequence of input pulses e(u) with different magnitude (and colors).
The output is the sum at each time t of the delayed pulse reponses h(t-u), weigthed by the corresponding magnitude e(u).
The input could be an electronic signal propagating on a line, the output would be the received signal.
The input could be the petrol flowing from a ship, the output would be the pollution versus time arriving on the beach !!