Metrics for Power Spectra: An Axiomatic Approach
2009 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 3, 859-867 p.Article in journal (Refereed) Published
We present an axiomatic framework for seeking distances between power spectral density functions. The axioms require that the sought metric respects the effects of additive and multiplicative noise in reducing our ability to discriminate spectra, as well as they require continuity of statistical quantities with respect to perturbations measured in the metric. We then present a particular metric which abides by these requirements. The metric is based on the Monge-Kantorovich transportation problem and is contrasted with an earlier Riemannian metric based on the minimum-variance prediction geometry of the underlying time-series. It is also being compared with the more traditional Itakura-Saito distance measure, as well as the aforementioned prediction metric, on two representative examples.
Place, publisher, year, edition, pages
2009. Vol. 57, no 3, 859-867 p.
Geodesics, geometry of spectral measures, metrics, power spectra, spectral distances
IdentifiersURN: urn:nbn:se:kth:diva-24140DOI: 10.1109/TSP.2008.2010009ISI: 000263431900004ScopusID: 2-s2.0-61549088710OAI: oai:DiVA.org:kth-24140DiVA: diva2:344080
QC 201008172010-08-172010-08-172010-08-17Bibliographically approved