  We investigate the statistical properties of the Barkhausen noise in
amorphous ferromagnetic films with thicknesses in the range between $100$ and
$1000$ nm. From Barkhausen noise time series measured with the traditional
inductive technique, we perform a wide statistical analysis and establish the
scaling exponents $\tau$, $\alpha$, $1/\sigma \nu z$, and $\vartheta$. We also
focus on the average shape of the avalanches, which gives further indications
on the domain wall dynamics. Based on experimental results, we group the
amorphous films in a single universality class, characterized by scaling
exponents $\tau\sim 1.27$, $\alpha \sim 1.5$, $1/\sigma \nu z \sim \vartheta
\sim 1.77$, values similar to that obtained for several bulk amorphous magnetic
materials. Besides, we verify that the avalanche shape depends on the
universality class. By considering the theoretical models for the dynamics of a
ferromagnetic domain wall driven by an external magnetic field through a
disordered medium found in literature, we interpret the results and identify an
experimental evidence that these amorphous films, within this thickness range,
present a typical three-dimensional magnetic behavior with predominant
short-range elastic interactions governing the domain wall dynamics. Moreover,
we provide experimental support for the validity of a general scaling form for
the average avalanche shape for non-mean-field systems.
