Kullback-Leibler approximation of spectral density functions

Tryphon T Georgiou, Anders Lindquist

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


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 ψ by one that is consistent with prescribed second-order statistics. In particular, we show (i) that there is a unique spectral density φ which minimizes this Kullback-Leibler distance, (ii) that this optimal approximate is of the form ψ/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 ψ = 1, the convex functional becomes quadratic and the solution is then specified by linear equations.

Original languageEnglish (US)
Pages (from-to)4237-4242
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - Dec 1 2003
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: Dec 9 2003Dec 12 2003

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