INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
Aliasing and oblique dual pair designs for consistent sampling
MARÍA JOSÉ BENAC; PEDRO MASSEY; DEMETRIO STOJANOFF
LINEAR ALGEBRA AND ITS APPLICATIONS
ELSEVIER SCIENCE INC
Lugar: Amsterdam; Año: 2015 vol. 487 p. 112 - 112
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 oblique duality, within the context of consistent sampling.