The Shannon sampling theorem - Its various extensions and applications: A tutorial review
Abstract
A clear statement of Shannon's sampling theorem is given and its origin as Whittaker's interpolation series is discussed. Extensions of the theorem are considered including sampling for functions of more than one variable, random processes, nonuniform sampling, nonband-limited functions, implicit sampling, generalized functions (distributions) and sampling for general integral transforms. The error analysis of the various sampling expansions, including specific error bounds for the truncation, aliasing, jitter and parts of various other errors, is discussed.
- Publication:
-
IEEE Proceedings
- Pub Date:
- November 1977
- Bibcode:
- 1977IEEEP..65.1565J
- Keywords:
-
- Data Sampling;
- Error Analysis;
- Information Theory;
- Random Processes;
- Whittaker Functions;
- Bibliographies;
- Communication Theory;
- Extremum Values;
- Integral Transformations;
- Interpolation;
- Mathematical Models;
- Shannon-Wiener Measure;
- Theorems;
- Truncation Errors;
- Communications and Radar