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تسجيل مستخدم جديدAliasing and oblique dual pair designs for consistent sampling
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In this paper we study some aspects of oblique duality between finite sequences of vectors $cF$ and $cG$ lying in finite dimensional subspaces $cW$ and $cV$, respectively. We compute the possible eigenvalue lists of the frame operators of oblique duals to $cF$ lying in $cV$; we then compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for $cF$ under some restrictions. We obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces $cV$ and $cW$ has in oblique duality. We apply this analysis to compute those rigid rotations $U$ for $cW$ such that the canonical oblique dual of $Ucdot cF$ minimize every convex potential; we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations $U$ for $cW$ such that the canonical oblique dual pair associated to $Ucdot cF$ minimize the aliasing. We point out that these two last problems are intrinsic to the theory of oblique duality.
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