Generalized sampling: from shift-invariant to U-invariant spaces Articles uri icon

authors

  • FERNANDEZ MORALES, HECTOR RAUL
  • GARCIA GARCIA, ANTONIO
  • HERNANDEZ MEDINA, MIGUEL ANGEL
  • MUÑOZ BOUZO, MARIA JOSE

publication date

  • May 2015

start page

  • 303

end page

  • 329

issue

  • 3 (303)

volume

  • 13

International Standard Serial Number (ISSN)

  • 0219-5305

Electronic International Standard Serial Number (EISSN)

  • 1793-6861

abstract

  • The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U.

keywords

  • stationary sequences; u-invariant subspaces; frames; dual frames; time-jitter error; group of unitary operators; pseudo-dual frames