Sampling theory: From Shannon sampling theorem to compressing sampling

Abstract

It is known that sampling theory lies at the heart of signal processing devices and communication systems. This study presents an account of the current state of sampling theorem after Shannon's formulation of the sampling theorem. Our emphasis is on some new tends of sampling theory in recent decade. At first, the problem of vector sampling expansion is argued. Secondly, signal reconstruction from local averages is showed. Thirdly, the issue of sampling theorem in the wavelet subspaces is investigated and some results are given. At last, compressed sampling and its two principles are reviewed. © 2010 Asian Network for Scientific Information.