Sampling and Reconstruction in a Shift Invariant Space with Multiple Generators

Abstract

The aim of this paper is to study sampling and reconstruction in a shift invariant space with multiple generators. On contrary to the classical case of a shift invariant space with a single generator, it is shown that cannot be a stable set of sampling for where when Further the problems of perturbation of a stable set of sampling and local reconstruction method are discussed along with an illustration and implementation.

Keywords:

• Frames
• Laurent operator
• Moore–Penrose inverse
• Riesz basis
• shift invariant space
• Wiener amalgam space

2010 Mathematics Subject Classification:

• 42C15
• 94A20

Acknowledgments

We thank the referee for meticulously reading our manuscript, pointing out many inaccuracies and giving us several valuable suggestions to improve the initial version of the manuscript to the present stage.