  Studying the jamming transition of granular and colloidal systems, has lead
to a proliferation of theoretical and numerical results formulated in the
language of the eigenspectrum of the dynamical matrix for these disordered
system. Only recently however, these modes have been accessed experimentally in
colloidal and granular media, computing the eigenmodes of the covariance matrix
of the particle positions. At the same time new conceptual and methodological
questions have appeared, regarding the interpretation of these results. In the
present paper, we first give an overview of the theoretical framework which is
appropriate to discuss the interpretation of the eigenmodes and eigenvalues of
the correlation matrix in terms of the vibrational properties of these systems.
  We then illustrate several aspects of the statistical and data analysis
techniques which are necessary to extract reliable results from experimental
data. Concentrating on the case of hard sphere simulations, colloidal and
granular experiments, we discuss how to test the existence of a metastable
state, the statistical independence of the sampling, the effect of the
experimental resolution, and the harmonic hypothesis underlying the approach,
highlighting both its promises and limitations.
