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Using a natural deconvolution for analysis of perturbed integer sampling in shift-invariant spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2011 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 373, no 1, 271-286 p.Article in journal (Refereed) Published
Abstract [en]

An important cornerstone of both wavelet and sampling theory is shift-invariant spaces, that is, spaces V spanned by a Riesz basis of integer-translates of a single function. Under some mild differentiability and decay assumptions on the Fourier transform of this function, we show that V also is generated by a function ϕ with Fourier transform equal to the convolution of g with the characteristic function living on the interval [-pi,pi]. We explain why analysis of this particular generating function can be more likely to provide large jitter bounds ε such that any f ∈ V can be reconstructed from perturbed integer samples f(k + ε_k) whenever the supremum of |ε_k| is smaller than ε. We use this natural deconvolution to further develop analysis techniques from a previous paper. Then we demonstrate the resulting analysis method on the class of spaces for which g has compact support and bounded variation (including all spaces generated by Meyer wavelet scaling functions), on some particular choices of ϕ for which we know of no previously published bounds and finally, we use it to improve some previously known bounds for B-spline shift-invariant spaces.

Place, publisher, year, edition, pages
2011. Vol. 373, no 1, 271-286 p.
Keyword [en]
Information technology - Signal processing
Keyword [sv]
Informationsteknik - Signalbehandling
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7744DOI: 10.1016/j.jmaa.2010.07.021Local ID: 62881050-904d-11df-8806-000ea68e967bOAI: oai:DiVA.org:ltu-7744DiVA: diva2:980634
Note
Validerad; 2011; 20100715 (grip)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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Ericsson, StefanGrip, Niklas

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