  In this work, a study of epitaxial growth was carried out by means of
wavelets formalism. We showed the existence of a dynamic scaling form in
wavelet discriminated linear MBE equation where diffusion and noise are the
dominant effects. We determined simple and exact scaling functions involving
the scale of the wavelets when the system size is set to infinity. Exponents
were determined for both, correlated and uncorrelated noise. The wavelet
methodology was applied to a computer model simulating the linear epitaxial
growth; the results showed a very good agreement with analytical formulation.
We also considered epitaxial growth with the additional Ehrlich$-$Schwoebel
effect. We characterized the coarsening of mounds formed on the surface during
the nonlinear phase using the wavelet power spectrum. The latter have an
advantage over other methods in the sense that one can track the coarsening in
both frequency (or scale) space and real space simultaneously. We showed that
the averaged wavelet power spectrum (also called scalegram) over all the
positions on the surface profile, identified the existence of a dominant scale
$a^*$, which increases with time following a power law relation of the form
$a^* \sim t^n$, where $n\simeq 1/3$.
