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Kullback-Leibler approximation of spectral density functions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-2681-8383
2003 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, Vol. 49, no 11, 2910-2917 p.Article in journal (Refereed) Published
Abstract [en]

We introduce a Kullback-Leibler-type distance between spectral density functions of stationary stochastic processes and solve the problem of optimal approximation of a given spectral density P by one that is consistent with prescribed second-order statistics. In general, such statistics are expressed as the state covariance of a linear filter driven by a stochastic process whose spectral density is sought. In this context, we show i) that there is a unique spectral density P which minimizes this Kullback-Leibler distance, ii) that this optimal approximate is of the form psi/Q where the "correction term" Q is a rational spectral density function, and iii) that the coefficients of Q can be obtained numerically by solving a suitable convex optimization problem. In the special case where psi = 1, the convex functional becomes quadratic and the solution is then specified by linear equations.

Place, publisher, year, edition, pages
2003. Vol. 49, no 11, 2910-2917 p.
Keyword [en]
approximation of power spectra, cross-entropy minimization, Kullback-Leibler distance, mutual information, optimization, spectral, estimation, nevanlinna-pick interpolation, degree constraint, maximum-entropy, covariance, identification, algorithms, sequences
National Category
Mathematics Signal Processing
URN: urn:nbn:se:kth:diva-22968DOI: 10.1109/tit.2003.819324ISI: 000186618500008OAI: diva2:341666
QC 20100525 NR 20140804Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2012-01-16Bibliographically approved

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