  We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, in
which a uniform light signal is emitted on the $r$-level surface of the
cosmological time for $r\to 0$. We show that the frequency of this signal, as
perceived by a fixed observer, is a well-defined, bounded function which is
generally not continuous. This defines a model with anisotropic background
radiation that contains information about initial singularity of the spacetime.
In dimension 2+1, we show that this observed frequency function is stable under
suitable perturbations of the spacetime, and that, under certain conditions, it
contains sufficient information to recover its geometry and topology. We
compute an approximation of this frequency function for a few simple examples.
