Digital Signal Processing in Cosmology
  We address the problem of discretizing continuous cosmological signals such
as a galaxy distribution for further processing with Fast Fourier techniques.
Discretizing, in particular representing continuous signals by discrete sets of
sample points, introduces an enormous loss of information, which has to be
understood in detail if one wants to make inference from the discretely sampled
signal towards actual natural physical quantities. We therefore review the
mathematics of discretizing signals and the application of Fast Fourier
Transforms to demonstrate how the interpretation of the processed data can be
affected by these procedures. It is also a well known fact that any practical
sampling method introduces sampling artifacts and false information in the form
of aliasing. These sampling artifacts, especially aliasing, make further
processing of the sampled signal difficult. For this reason we introduce a fast
and efficient supersampling method, frequently applied in 3D computer graphics,
to cosmological applications such as matter power spectrum estimation. This
method consists of two filtering steps which allow for a much better
approximation of the ideal sampling procedure, while at the same time being
computationally very efficient.Thus, it provides discretely sampled signals
which are greately cleaned from aliasing contributions.
