A method with error estimates for band-limited signal extrapolation from inaccurate data

Xiang Gen Xia*, M. Zuhair Nashed

*Corresponding author for this work

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Abstract

In this paper, we consider the problem of extrapolation of a band-limited signal outside a fixed interval from its (approximate or contaminated) values in that interval. We propose a new extrapolation method that estimates the error between the extrapolated and true values, and which also resolves the ill-posedness of the problem. The method is called a modified minimum norm solution (MMNS) method. Both the continuous MMNS and its discretization are studied. The error estimates hold for some classes of band-limited signals, when the maximum magnitude of the data error is known. These classes of band-limited signals are also characterized.

Original languageEnglish
Pages (from-to)1641-1659
Number of pages19
JournalInverse Problems
Volume13
Issue number6
DOIs
Publication statusPublished - 1997
Externally publishedYes

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Xia, X. G., & Zuhair Nashed, M. (1997). A method with error estimates for band-limited signal extrapolation from inaccurate data. Inverse Problems, 13(6), 1641-1659. https://doi.org/10.1088/0266-5611/13/6/015