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Spectral analysis of nonuniformly sampled data: a new approach versus the periodogram
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2009 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 3, 843-858 p.Article in journal (Refereed) Published
Abstract [en]

We begin by revisiting the periodogram to explain why arguably the  plain least-squares periodogram (LSP) is preferable to the "classical"  Fourier periodogram, from a data-fitting viewpoint, as well as to the  frequently-used form of LSP due to Lomb and Scargle, from a  computational standpoint. Then we go on to introduce a new enhanced  method for spectral analysis of nonuniformly sampled data sequences.  The new method can be interpreted as an iteratively weighted LSP that  makes use of a data-dependent weighting matrix built from the most  recent spectral estimate. Because this method is derived for the case  of real-valued data (which is typically more complicated to deal with  in spectral analysis than the complex-valued data case), it is  iterative and it makes use of an adaptive (i.e., data-dependent)  weighting, we refer to it as the real-valued iterative adaptive  approach (RIAA). LSP and RIAA are nonparametric methods that can be  used for the spectral analysis of general data sequences with both  continuous and discrete spectra. However, they are most suitable for  data sequences with discrete spectra (i.e., sinusoidal data), which is  the case we emphasize in this paper. AB We begin by revisiting the periodogram to explain why arguably the  plain least-squares periodogram (LSP) is preferable to the "classical"  Fourier periodogram, from a data-fitting viewpoint, as well as to the  frequently-used form of LSP due to Lomb and Scargle, from a  computational standpoint. Then we go on to introduce a new enhanced  method for spectral analysis of nonuniformly sampled data sequences.  The new method can be interpreted as an iteratively weighted LSP that  makes use of a data-dependent weighting matrix built from the most  recent spectral estimate. Because this method is derived for the case  of real-valued data (which is typically more complicated to deal with  in spectral analysis than the complex-valued data case), it is  iterative and it makes use of an adaptive (i.e., data-dependent)  weighting, we refer to it as the real-valued iterative adaptive  approach (RIAA). LSP and RIAA are nonparametric methods that can be  used for the spectral analysis of general data sequences with both  continuous and discrete spectra. However, they are most suitable for  data sequences with discrete spectra (i.e., sinusoidal data), which is  the case we emphasize in this paper.

Place, publisher, year, edition, pages
2009. Vol. 57, no 3, 843-858 p.
Keyword [en]
BIC, iterative adaptive approach, least-squares method, nonuniformly, sampled data, periodogram, spectral analysis
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:uu:diva-104503DOI: 10.1109/TSP.2008.2008973ISI: 000263431900003OAI: oai:DiVA.org:uu-104503DiVA: diva2:219860
Available from: 2009-05-28 Created: 2009-05-28 Last updated: 2017-12-13Bibliographically approved

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Stoica, Peter

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