  The linear response of synchronized time-delayed chaotic systems to small
external perturbations, i.e., the phenomenon of chaos pass filter, is
investigated for iterated maps. The distribution of distances, i.e., the
deviations between two synchronized chaotic units due to external perturbations
on the transfered signal, is used as a measure of the linear response. It is
calculated numerically and, for some special cases, analytically. Depending on
the model parameters this distribution has power law tails in the region of
synchronization leading to diverging moments of distances. This is a
consequence of multiplicative and additive noise in the corresponding linear
equations due to chaos and external perturbations. The linear response can also
be quantified by the bit error rate of a transmitted binary message which
perturbs the synchronized system. The bit error rate is given by an integral
over the distribution of distances and is calculated analytically and
numerically. It displays a complex nonmonotonic behavior in the region of
synchronization. For special cases the distribution of distances has a fractal
structure leading to a devil's staircase for the bit error rate as a function
of coupling strength. The response to small harmonic perturbations shows
resonances related to coupling and feedback delay times. A bi-directionally
coupled chain of three units can completely filtered out the perturbation. Thus
the second moment and the bit error rate become zero.
