Title

Kramer'S Sampling Theorem For Multidimensional Signals And Its Relationship With Lagrange-Type Interpolations

Keywords

an N-dimensional Paley-Wiener interpolation theorem for band-limited signals and multidimensional Lagrange interpolation; Shannon and Kramer sampling theorems in N dimensions

Abstract

Kramer's sampling theorem, which is a generalization of the Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem, enables one to reconstruct functions that are integral transforms of types other than the Fourier one from their sampled values. In this paper, we generalize Kramer's theorem to N dimensions (N ≥ 1) and show how the kernel function and the sampling points in Kramer's theorem can be generated. We then investigate the relationship between this generalization of Kramer's theorem and N-dimensional versions of both the WSK theorem and the Paley-Wiener interpolation theorem for band-limited signals. It is shown that the sampling series associated with this generalization of Kramer's theorem is nothing more than an N-dimensional Lagrange-type interpolation series. © 1992 Kluwer Academic Publishers.

Publication Date

10-1-1992

Publication Title

Multidimensional Systems and Signal Processing

Volume

3

Issue

4

Number of Pages

323-340

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/BF01940228

Socpus ID

0010935857 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0010935857

This document is currently not available here.

Share

COinS