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 - 145

0024-3795

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