  In this paper, we study the amplification of weak frequency dependent signals
in the CMB sky due to their cross correlation to intrinsic anisotropies. In
particular, we center our attention on mechanisms generating some weak signal,
of peculiar spectral behaviour, such as resonant scattering in ionic, atomic or
molecular lines, thermal SZ effect or extragalactic foreground emissions, whose
typical amplitude (denoted by $\epsilon$) is sufficiently smaller than the
intrinsic CMB fluctuations. We find that all these effects involve either the
autocorrelation of anisotropies generated during recombination ($z_{rec}$) or
the cross-correlation of those anisotropies with fluctuations arising at some
later redshift $z_i$. The degree of this correlation can be computed under the
assumption that density fluctuations were generated as standard inflationary
models dictate and that they evolved in time according to linear theory. In
case that the weak signal is frequency dependent, we show that, by substracting
power spectra at different frequencies, it is possible to avoid the limit
associated to Cosmic Variance and unveil weaker terms linear in $\epsilon$. We
find that the correlation term shows a different spectral dependence than the
squared ($\propto \epsilon^2$) term considered usually, making its extraction
particularly straightforward for the thermal SZ effect. Furthermore, we find
that in most cases the correlation terms are particularly relevant at low
multipoles and must be taken into account when characterising the power
spectrum associated to weak signals in the large angular scales.
