This example is great, hope you don't mind if I spell it out how your impulse weight f(d) and impulse response functions g(d) are functions over d (each associated with 10^d):

  f(0) = 1      g(0) = 3      f*g(0) = 3 
  f(1) = 0      g(1) = 2      f*g(1) = 2 
  f(2) = 1                    f*g(2) = 3 
  f(3) = 0                    f*g(3) = 2
  f(4) = 0                    f*g(4) = 0
  f(5) = 1                    f*g(5) = 3 
                              f*g(6) = 2

You can see how when there is an impulse weight "x" in digit space entry d, the impulse response "3x" comes at d, and the impulse response "2x" comes at d+1. Note how f and g can be anything and it convolution (f * g) is still their multiplication (except for the obvious rub when f*g(d) is greater than 9, so you need to add a rule about that).