Title

A sampling theorem for signals bandlimited to a general domain in several dimensions

Abstract

Sampling series expansions for functions (signals) that are bandlimited to N-dimensional rectangles (N ≥ 1) have been studied extensively; however, if a function is bandlimited to a general region in RN, not much is known about its sampling series expansion. In this paper, we derive a sampling theorem for functions that are bandlimited (in the sense of Kramer) to finite regions with smooth boundaries in RN. The sampling series expansions obtained for these functions are Lagrange-type interpolation series. Our technique utilizes Green′s function of the region involved. As an application of our sampling theorem, we obtain a new method for summing infinite series in several variables. © 1994 Academic Press, Inc.

Publication Date

1-1-1994

Publication Title

Journal of Mathematical Analysis and Applications

Volume

187

Issue

1

Number of Pages

196-211

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1006/jmaa.1994.1352

Socpus ID

39449095466 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/39449095466

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