New directions in sampling and multi-rate A-D conversion via number theoretic methods

Number theoretic methods have been used in the study of harmonic analysis to extend existing theories and develop new approaches to both theoretical and applied problems. A specific example of this approach is in the development of sampling theory on non-commensurate lattices. We will construct examples of these lattices, and use a generation of B. Ya. Levin's sine-type functions to develop interpolating formulae on these lattices. We then consider application of these new sampling results to multi-rate AU conversion.