TY - JOUR

T1 - Kullback-Leibler approximation of spectral density functions

AU - Georgiou, Tryphon T

AU - Lindquist, Anders

PY - 2003/12/1

Y1 - 2003/12/1

N2 - 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.

AB - 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.

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M3 - Conference article

AN - SCOPUS:1542319143

VL - 4

SP - 4237

EP - 4242

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

T2 - 42nd IEEE Conference on Decision and Control

Y2 - 9 December 2003 through 12 December 2003

ER -