We
now interpret the convolution (x*h)(t) as the common
(shaded) area enclosed under the curves x(v) and
h(t-v) as v varies over the entire real axis.
x(v) is the given input function, with the independent
variable now called v. h(t-v) is the impulse response
obtained by inverting h(v) and then shifting it by
t
units on the v-axis.
As t increases clearly h(t-v) can be considered to be
a train moving towards the right, and at each point on
the v-axis,
the area under the product x(v) and h(t-v) is the value of
y(t) at that t.
