Vector sampling expansions in shift invariant subspaces

Abstract

Multi-input multi-output (MIMO) sampling scheme which is motivated by applications in multi-channel deconvolution and multi-source separation has been investigated in many aspects. Common for most of results on MIMO systems is that the input signals are supposed to be band-limited. In this paper, we study vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a vector sampling theorem to hold are given. We also give several examples to illustrate the main result.

Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling Theory

“…Applying the isomorphism T U,Φ in (20) we obtain that any f = T U,Φ x ∈ V Φ can be recovered from data {L m f (h)} h∈H; m=1,2,...,M by means of the sampling formula…”

Multivariate vector sampling expansion in shift-invariant subspaces

“…Aldroubi et al (2005), García and Pérez-Villalón (2009) and García and Pérez-Villalón (2006) considered sampling theorems on a multivariate finitely generated shift-invariant subspace. Shang et al (2007) gave some equivalence conditions for sampling theorems on a univariate vector shiftinvariant subspace. However, to the best of our knowledge, there are no results published about sampling theorems for a multivariate vector shift-invariant subspace.…”

Vector sampling theorem for wavelet subspaces

“…Definition 2.1 [10] Suppose that {ϕ (t − k) , k ∈ Z} is a Riesz (stable) basis for shift invariant subspace V 0 , which is generated by {ϕ (t − k) , k ∈ Z}. Then, there exist two constants A and B, 0 < A B < +∞, such…”