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Journal of Convex Analysis 17 (2010), No. 2, 381--403
Copyright Heldermann Verlag 2010

Properties of the Convex Cone of Vectors with Autocorrelated Components

Marc Fuentes
INRIA Nancy Grand Est, 615 Rue du Jardin Botanique, 54602 Villers les Nancy, France

This paper reviews some properties of the set of vectors with autocorrelated components. This set appears in some signal processing problems, in particular filter synthesis or statistical estimation. It turns out to be a closed convex cone enjoying several representations and various geometrical properties. The aim of this paper is to gather different aspects of the geometry of this cone. We adopt a convex analysis point of view to present known and new results.

Keywords: Convex analysis, autocorrelation, nonnegative trigonometric polynomials.

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