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Generalized sampling in shift invariant spaces with frames

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Abstract

Generalized sampling in a shift invariant subspace V of L 2(ℝ) is considered. A function f in V is processed with different filters L m and then one tries to reconstruct f from the samples L m f(j′k). We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question: How to obtain dual frames with compact support?

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Authors and Affiliations

  1. Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87, Luleå, Sweden

    Stefan Ericsson

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  1. Stefan Ericsson
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Correspondence to Stefan Ericsson.

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Ericsson, S. Generalized sampling in shift invariant spaces with frames. Acta. Math. Sin.-English Ser. 28, 1823–1844 (2012). https://doi.org/10.1007/s10114-012-1235-4

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  • DOI: https://doi.org/10.1007/s10114-012-1235-4

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