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Title
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VEXPA : Validated EXPonential Analysis through regular sub-sampling
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Author
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Abstract
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| In signal processing data are traditionally sampled according to the Shannon-Nyquist theorem in order to prevent aliasing effects. Here we focus on parametric methods and introduce a procedure that allows these methods to work with sub-sampled data. We actually make use of the aliasing effect to regularize the problem statement rather than that we avoid it. The new approach adds a number of features to a standard exponential analysis, among which output validation, the automatic detection of the exponential model order, robustness against outliers, and the possibility to parallelize the analysis. In Section 2 the standard exponential analysis is described, including a sensitivity analysis. In Section 3 the ingredients for the new technique are elaborated, of which good use is made in Section 4 where we essentially bring everything together in what we call VEXPA. Some numerical examples of the new procedure in Section 5 illustrate that the additional features are indeed realized and that VEXPA is a valuable add-on to any stand-alone exponential analysis. While returning a lot of additional output, it maintains the comparison to the CRLB of the underlying method, for which we here choose ESPRIT. |
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Language
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English
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Source (journal)
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Arxiv
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Publication
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2018
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Volume/pages
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17 p.
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Full text (open access)
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