  The paper develops a method for discrete computational Fourier analysis of
functions defined on quasicrystals and other almost periodic sets. A key point
is to build the analysis around the emerging theory of quasicrystals and
diffraction in the setting on local hulls and dynamical systems. Numerically
computed approximations arising in this way are built out of the Fourier module
of the quasicrystal in question, and approximate their target functions
uniformly on the entire infinite space.
  The methods are entirely group theoretical, being based on finite groups and
their duals, and they are practical and computable. Examples of functions based
on the standard Fibonacci quasicrystal serve to illustrate the method (which is
applicable to all quasicrystals modeled on the cut and project formalism).
