MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS-Reference-Cited by-同舟云学术

MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS

Published:2012-01 Issue:01 Volume:10 Page:1250003
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

GARCIA A. G.¹,KIM J. M.²,KWON K. H.³,YOON G. J.⁴

Affiliation:

1. Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganes, Madrid, 28911, Spain

2. Department of Bio and Brain Engineering, KAIST, Daejeon 305-701, Korea

3. Department of Mathematical Sciences, KAIST, Daejeon 305-701, Korea

4. National Institute of Mathematical Sciences, Daejeon 305-340, Korea

Abstract

Let φ be a continuous function in L2(ℝ) such that the sequence {φ(t - n)}n∈ℤ is a frame sequence in L2(ℝ) and assume that the shift-invariant space V(φ) generated by φ has a multi-banded spectrum σ(V). The main aim in this paper is to derive a multi-channel sampling theory for the shift-invariant space V(φ). By using a type of Fourier duality between the spaces V(φ) and L2[0, 2π] we find necessary and sufficient conditions allowing us to obtain stable multi-channel sampling expansions in V(φ).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691311004456

Reference24 articles.

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