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2009•Integral Transforms and Special FunctionsRequires access

Fourier and Hankel bandlimited signal recovery

Tahar Moumni, Abderrazek Karoui

Open publisher page 8 citations

Abstract

In this paper, we study the recovery problem of a bandlimited signal with missing data. More precisely, given a Fourier bandlimited signal f with bandwidth W and unknown on a bounded measurable set T, then by using the theory of prolate spheroidal wave functions, we prove that f can be stably recovered, no matter how large the Lebesgue measure of T. Moreover,we generalize these results to the case of Hankel bandlimited signals.

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What this paper is about

In this paper, we study the recovery problem of a bandlimited signal with missing data. More precisely, given a Fourier bandlimited signal f with bandwidth W and unknown on a bounded measurable set T, then by using the theory of prolate spheroidal wave functions, we prove that f can be stably recovered, no matter how large the Lebesgue measure of T. Moreover,we generalize these results to the case of Hankel bandlimited signals.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study the recovery problem of a bandlimited signal with missing data. More precisely, given a Fourier bandlimited signal f with bandwidth W and unknown on a bounded measurable set T, then by using the theory of prolate spheroidal wave functions, we prove that f can be stably recovered, no matter how large the Lebesgue measure of T. Moreover,we generalize these results to the case of Hankel bandlimited signals.

Key concepts: Bandlimiting, Mathematics, Fourier transform, Bounded function, Hankel transform, Lebesgue measure, Mathematical analysis, SIGNAL (programming language)

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