  The average shape of the pulse in Barkhausen noise has been recently proposed
as a tool to compare models and experiments. We compute theoretically the pulse
shape of Barkhausen noise in a model describing the motion of a domain wall in
an effective Brownian potential. In this framework, the pulse shape is related
to the properties of the excursion of a random process in a $c\log(x)-kx$
potential. We record the Barkhausen noise in polycristalline ${FeSi}$
materials, and compare the pulse shape with the one predicted by the domain
wall model.
