Rational approximations of spectral densities based on the Alpha divergence
Abstract
We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints corresponding to imposing the given second-order statistics. Here, we consider the Alpha divergence family as a distance measure. We show that the corresponding approximation problem leads to a family of rational solutions. Secondly, such a family contains the solution which generalizes the Kullback-Leibler solution proposed by Georgiou and Lindquist in 2003. Finally, numerical simulations suggest that this family contains solutions close to the non-rational solution given by the principle of minimum discrimination information.
Keywords
Cite
@article{arxiv.1302.5131,
title = {Rational approximations of spectral densities based on the Alpha divergence},
author = {Mattia Zorzi},
journal= {arXiv preprint arXiv:1302.5131},
year = {2013}
}
Comments
to appear in the Mathematics of Control, Signals, and Systems