By Topic

Distances and Riemannian Metrics for 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
$33 $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

1 Author(s)
Tryphon T. Georgiou ; Univ. of Minnesota, Minneapolis

We introduce a differential-geometric structure for spectral density functions of discrete-time random processes. This is quite analogous to the Riemannian structure of information geometry, which is used to study perturbations of probability density functions, and which is based on the Fisher information metric. Herein, we introduce an analogous Riemannian metric, which we motivate with a problem in prediction theory. It turns out that this problem also provides a prediction theoretic interpretation to the Itakura distortion measure, which relates to our metric. Geodesies and geodesic distances are characterized in closed form and, hence, the geodesic distance between two spectral density functions provides an explicit, intrinsic (pseudo)metric on the cone of density functions. Certain other distortion measures that involve generalized means of spectral density functions are shown to lead to the same Riemannian metric. Finally, an alternative Riemannian metric is introduced, which is motivated by an analogous problem involving smoothing instead of prediction.

Published in:

IEEE Transactions on Signal Processing  (Volume:55 ,  Issue: 8 )