  In this paper we give a multiresolution construction in Bergman space. The
successful application of rational orthogonal bases needs a priori knowledge of
the poles of the transfer function that may cause a drawback of the method. We
give a set of poles and using them we will generate a multiresolution in $A^2$.
We study the upper and lower density of this set, and we give sufficient
conditions for this set to be interpolating or sampling sequence for the
Bergman space. The construction is an analogy with the discrete affine
wavelets, and in fact is the discretization of the continuous voice transform
generated by a representation of the Blaschke group over the Bergman space. The
constructed discretization scheme gives opportunity of practical realization of
hyperbolic wavelet representation of signals belonging to the Bergman space if
we can measure their values on a given set of points inside the unit disc.
Convergence properties of the hyperbolic wavelet representation will be
studied.
