By Topic

Kullback-Leibler approximation of spectral density functions

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Georgiou, T.T. ; Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN, USA ; Lindquist, A.

We introduce a Kullback-Leibler (1968) -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 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 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 11 )