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Identifiability and well-posedness of shaping-filter parameterizations: A global analysis approach
KTH, Superseded Departments, Mathematics.
KTH, Superseded Departments, Mathematics.
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-2681-8383
2002 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 41, no 1, 23-59 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we study the well-posedness of the problems of determining shaping filters from combinations of finite windows of cepstral coefficients, covariance lags, or Markov parameters. For example, we determine whether there exists a shaping filter with a prescribed window of Markov parameters and a prescribed window of covariance lags. We show that several such problems are well-posed in the sense of Hadamard; that is, one can prove existence, uniqueness (identifiability), and continuous dependence of the model on the measurements. Our starting point is the global analysis of linear systems, where one studies an entire class of systems or models as a whole, and where one views measurements, such as covariance lags and cepstral coefficients or Markov parameters, from data as functions on the entire class. This enables one to pose such problems in a way that tools from calculus, optimization, geometry, and modern nonlinear analysis can be used to give a rigorous answer to such problems in an algorithm-independent fashion. In this language, we prove that a window of cepstral coefficients and a window of covariance coefficients yield a bona de coordinate system on the space of shaping filters, thereby establishing existence, uniqueness, and smooth dependence of the model parameters on the measurements from data.

Place, publisher, year, edition, pages
2002. Vol. 41, no 1, 23-59 p.
Keyword [en]
identifiability, parameterization, well-posedness, foliations, Caratheodory extension, spectral estimation, cepstrum, NEVANLINNA-PICK INTERPOLATION, CEPSTRAL COEFFICIENTS, COVARIANCE EXTENSION, REALIZATION PROBLEM, DEGREE CONSTRAINT
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-13173DOI: 10.1137/S0363012900383077ISI: 000176312200002OAI: oai:DiVA.org:kth-13173DiVA: diva2:321480
Note
QC 20100601Available from: 2010-06-01 Created: 2010-06-01 Last updated: 2010-06-01Bibliographically approved
In thesis
1. Spectral Estimation by Geometric, Topological and Optimization Methods
Open this publication in new window or tab >>Spectral Estimation by Geometric, Topological and Optimization Methods
2001 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH, 2001. xii, 32 p.
Series
Trita-MAT, ISSN 1401-2286 ; 01-OS-03
Keyword
Spectral Estimation, ARMA models, Covariance analysis, Cepstral analysis, Markov parameters, Global analysis, Convex Optimization, Continuation methods, Entropy maximization
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-3118 (URN)
Public defence
2001-04-06, 00:00 (English)
Note
QC 20100601Available from: 2001-03-29 Created: 2001-03-29 Last updated: 2010-06-01Bibliographically approved

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Lindquist, Anders

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