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

    Authors

    A. I. Zayed

    Comments

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    Abbreviated Journal Title

    Multidimens. Syst. Signal Process.

    Keywords

    Shannon And Kramer Sampling Theorems In N-Dimensions; An N-Dimensional; Paley-Wiener Interpolation Theorem For Band-Limited Signals And; Multidimensional Lagrange Interpolation; Computer Science, Theory & Methods; Engineering, Electrical & Electronic

    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 greater-than-or-equal-to 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.

    Journal Title

    Multidimensional Systems and Signal Processing

    Volume

    3

    Issue/Number

    4

    Publication Date

    1-1-1992

    Document Type

    Article

    Language

    English

    First Page

    323

    Last Page

    340

    WOS Identifier

    WOS:A1992JP78700002

    ISSN

    0923-6082

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