A Sampling Theorem For Signals Band-Limited To A General Domain In Several Dimensions

    Authors

    A. I. Zayed

    Comments

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    Abbreviated Journal Title

    J. Math. Anal. Appl.

    Keywords

    STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; Mathematics, Applied; Mathematics

    Abstract

    Sampling series expansions for functions (signals) that are bandlimited to N-dimensional rectangles (N greater-than-or-equal-to 1) have been studied extensively; however, if a function is bandlimited to a general region in R(N), 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 R(N). 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. (C) 1994 Academic Press, Inc.

    Journal Title

    Journal of Mathematical Analysis and Applications

    Volume

    187

    Issue/Number

    1

    Publication Date

    1-1-1995

    Document Type

    Article

    Language

    English

    First Page

    196

    Last Page

    211

    WOS Identifier

    WOS:A1994PL38300012

    ISSN

    0022-247X

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