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Covariance interpolation and geometry of power spectral densities | IEEE Conference Publication | IEEE Xplore

Covariance interpolation and geometry of power spectral densities


Abstract:

When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimat...Show More

Abstract:

When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. There is an infinite family of power spectra consistent with such an estimate and in applications, such as identification, we want to single out the most representative spectrum. Here, we choose a prior spectral density to represent a priori information, and the spectrum closest to it in a given quasi-distance is determined. Depending on the selected quasi-distance, the geometry of the space of power spectral densities varies, and the structure of the minimizing spectral density changes with it. Recently, the Kullback-Leibler divergence, the Itakura-Saito divergence and Hellinger distances has been shown to determine power spectral densities of rational form and with tractable properties. Here, starting instead with the structure of the power spectral density, different (quasi-)distances and geometries for power spectral densities are derived.
Date of Conference: 23-26 August 2009
Date Added to IEEE Xplore: 02 April 2015
Print ISBN:978-3-9524173-9-3
Conference Location: Budapest, Hungary

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