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Generalizations of the sampling theorem: Seven decades after Nyquist

Vaidyanathan, P. P. (2001) Generalizations of the sampling theorem: Seven decades after Nyquist. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48 (9). pp. 1094-1109. ISSN 1057-7122. http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetcsI01

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Abstract

The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The connection between such extensions and the theory of filter banks in DSP has been well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples. Applications in multiresolution computation and in digital spline interpolation are also reviewed.


Item Type:Article
Additional Information:© 2001 IEEE. Reprinted with permission. Manuscript received April 16, 2000; revised March 23, 2001. This work was supported in part by the National Science Foundation under grant MIP-0703755, in part by the Office of Naval Research under grant N00014-99-1-1002, and in part by Microsoft Research, Redmond, WA. This paper has been presented in parts at conferences. This paper was recommended by Associate Editor M. O. Ahmad.
Subject Keywords:Bandlimited signals, FIR reconstruction, multiresolution, nonuniform sampling, sampling theorems
Record Number:CaltechAUTHORS:VAIieeetcsI01
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetcsI01
Alternative URL:http://dx.doi.org/10.1109/81.948437
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1442
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Jan 2006
Last Modified:26 Dec 2012 08:44

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