Computer Science – Systems and Control
Scientific paper
2012-01-21
Computer Science
Systems and Control
9 figures
Scientific paper
The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra, estimated from finite second-order statistics. The family of spectra consistent with given statistics represents the uncertainty set about the "true" power spectrum. Our aim is to quantify the size of this set using suitable notions of distance. In particular, the diameter of the set bounds the distance between an estimated nominal spectrum and the true spectrum. These perturbations of the true power spectrum will in general contain smooth spectra as well as spectra containing spectral lines, and hence, that they ought to be considered in the weak topology---the topology defined by continuity of moments. We give examples of such metrics that induce the weak topology and we discuss cases where we can specifically quantify spectral uncertainty by computing a priori bounds using covariance statistics. This allows, e.g., for selecting metrics suitable for specific purposes as regards to specifying the desired resolution in selected frequency bands. Finally, using this machinery, we show a spectral estimation example where we quantify the resolution gained by using a high resolution technique (THREE) compared to standard covariances estimates.
Georgiou Tryphon T.
Karlsson Johan
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