Home  |   Login  |   Logout  |   Access Information  |   Alerts  |   Purchase History  |   Cart  |   Sitemap  |   Help   
 
CrossRef Search
BROWSE SEARCH IEEE XPLORE GUIDE SUPPORT
You requested this document:
1. The Shannon sampling theorem—Its various extensions and applications: A tutorial review
Jerri, A.J.;
Proceedings of the IEEE
Volume 65,  Issue 11,  Nov. 1977 Page(s):1565 - 1596
Abstract:

It has been almost thirty years since Shannon introduced the sampling theorem to communications theory. In this review paper we will attempt to present the various contributions made for the sampling theorems with the necessary mathematical details to make it self-contained. We will begin by a clear statement of Shannon's sampling theorem followed by its applied interpretation for time-invariant systems. Then we will review its origin as Whittaker's interpolation series. The extensions will include sampling for functions of more than one variable, random processes, nonuniform sampling, nonband-limited functions, implicit sampling, generalized functions (distributions), sampling with the function and its derivatives as suggested by Shannon in his original paper, and sampling for general integral transforms. Also the conditions on the functions to be sampled will be summarized. The error analysis of the various sampling expansions, including specific error bounds for the truncation, aliasing, jitter and parts of various other errors will be discussed and summarized. This paper will be concluded by searching the different recent applications of the sampling theorems in other fields, besides communications theory. These include optics, crystallography, time-varying systems, boundary value problems, spline approximation, special functions, and the Fourier and other discrete transforms.
Abstract | Full Text: PDF(3343 KB)    IEEE JNL
 
» Key
IEEE JNL IEEE Journal or Magazine
IEE JNL IEE Journal or Magazine
IEEE CNF IEEE Conference Proceeding
IEE CNF IEE Conference Proceeding
IEEE STD IEEE Standard
 
 
Indexed by IEE Inspec
© Copyright 2008 IEEE – All Rights Reserved