  Recently we have shown that slow relaxations in the electron glass system can
be understood in terms of the spectrum of a matrix describing the relaxation of
the system close to a metastable state. The model focused on the electron glass
system, but its generality was demonstrated on various other examples. Here, we
study the noise spectrum in the same framework. We obtain a remarkable relation
between the spectrum of relaxation rates $\lambda$ described by the
distribution function $P(\lambda) \sim 1/\lambda$ and the $1/f$ noise in the
fluctuating occupancies of the localized electronic sites. This noise can be
observed using local capacitance measurements. We confirm our analytic results
using numerics, and also show how the Onsager symmetry is fulfilled in the
system.
