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Approximative Linear and Logarithmic Interpolation of Spectra
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2009 (English)Report (Other academic)
Abstract [en]

Given output data of a stationary stochastic process estimates of covariance and cepstrum parameters can be obtained. These estimates can be used to determine ARMA models to approximately fit the data by matching the parameters exactly. However, the estimates of the parameters may contain large errors, especially if they are determined from short data sequences, and thus it makes sense to match the parameters in an approximate way. Here we consider a convex method for solving an approximate linear and logarithmic spectrum interpolation problem while maximizing the entropy and penalize the quadratic deviation from the nominal parameters.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2009. , 25 p.
Series
TRITA-MAT. OS, ISSN 1401-2294 ; 09:02
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-39044OAI: oai:DiVA.org:kth-39044DiVA: diva2:439295
Note

QC 20110907

Available from: 2011-09-08 Created: 2011-09-07 Last updated: 2014-09-24Bibliographically approved
In thesis
1. Spectral Moment Problems: Generalizations, Implementation and Tuning
Open this publication in new window or tab >>Spectral Moment Problems: Generalizations, Implementation and Tuning
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xii, 10 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 11:06
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-39026 (URN)978-91-7501-087-8 (ISBN)
Public defence
2011-09-16, Sal F2, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110906Available from: 2011-09-06 Created: 2011-09-06 Last updated: 2011-09-08Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • Other locale
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Output format
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