  We discuss the application of wavelet transforms to a critical interface
model, which is known to provide a good description of Barkhausen noise in soft
ferromagnets. The two-dimensional version of the model (one-dimensional
interface) is considered, mainly in the adiabatic limit of very slow driving.
On length scales shorter than a crossover length (which grows with the strength
of surface tension), the effective interface roughness exponent $\zeta$ is
$\simeq 1.20$, close to the expected value for the universality class of the
quenched Edwards-Wilkinson model. We find that the waiting times between
avalanches are fully uncorrelated, as the wavelet transform of their
autocorrelations scales as white noise. Similarly, detrended size-size
correlations give a white-noise wavelet transform. Consideration of finite
driving rates, still deep within the intermittent regime, shows the wavelet
transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies.
This behavior is ascribed to intra-avalanche correlations.
