Metrics for Power Spectra: An Axiomatic Approach

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 qua...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2009-03, Vol.57 (3), p.859-867
Main Authors: Georgiou, T.T., Karlsson, J., Takyar, M.S.
Format: Article
Language:English
Subjects:
Additive noise
Applied mathematics
Applied sciences
Axioms
Context modeling
Continuity
Density
Density functional theory
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Geodesics
geometry of spectral measures
Information geometry
Information theory
Information, signal and communications theory
MATEMATIK
MATHEMATICS
metrics
Miscellaneous
Noise
Noise measurement
Noise reduction
Optimeringslära, systemteori
Optimization, systems theory
Power measurement
Power spectra
Signal and communications theory
Signal processing
Signal, noise
Spectra
spectral distances
Statistics
Telecommunications and information theory
Tillämpad matematik
Transportation
Transportation problem
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Summary: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.
ISSN:1053-587X
1941-0476
1941-0476
DOI:10.1109/TSP.2008.2010009