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Spectrum estimation by interpolation of covariances and cepstrum parameters in an exponential class of spectral densities
2006 (English)In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, 799-804 p.Conference paper (Refereed)
Abstract [en]

Given output data of a stationary stochastic process estimates of the covariances and cepstrum parameters can be obtained. Methods of moments have been applied to these parameters for designing ARMA processes, and it has been shown that these two sets of parameters in fact form local coordinates for the set of ARMA processes, but that some combinations of cepstrum parameters and covariances cannot be matched exactly within this class of processes. Therefore, another class of processes is considered in this paper in order to be able to match any combination of covariances and cepstrum parameters. The main result is that a process with spectral density of the form phi(z) = exp {Sigma(m)(k=0) p(k)(z(k) + z(-k))}/Sigma(n)(k=0) q(k)(z(k) + z(-k))/2 can always match given covariances and cepstrum parameters. This is proven using a fixed-point argument, and a non-linear least-squares problem is proposed for determining a solution.

Place, publisher, year, edition, pages
2006. 799-804 p.
, IEEE Conference on Decision and Control, ISSN 0191-2216 ; 1-14
National Category
Other Mathematics
URN: urn:nbn:se:kth:diva-42229DOI: 10.1109/CDC.2006.377793ISI: 000252251603058ISBN: 978-1-4244-0170-3OAI: diva2:446478
45th IEEE Conference on Decision and Control Location: San Diego, CA Date: DEC 13-15, 2006
QC 20111007Available from: 2011-10-07 Created: 2011-10-06 Last updated: 2011-10-07Bibliographically approved

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