Irwin and Joan Jacobs Center for Communication and Information Technologies on the Classical – and Not so Classical – Shannon Sampling Theorem

We proceed with our recently-introduced geometric approach to sampling of manifolds and investigate the relationship that exists between the classical, i.e. Shannon type, and geometric sampling concepts and formalism. Some aspects of coding and the Gaussian channel problem are considered. A geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse Code Modulation and Vector Quantization of Images are provided. An extension of our sampling scheme to a certain class of infinite dimensional manifolds is also considered. The relationship between real functions of bounded curvature and classical band-limited signals is investigated. 1. General background 1.