A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

García, A.G. and Hernandez Medina, Miguel Angel and Perez Villalon, Gerardo and Portal Ruiz, Alberto (2011). A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling. "Linear Algebra And Its Applications", v. 435 (n. 1); pp. 2837-2859. ISSN 0024-3795. https://doi.org/10.1016/j.laa.2011.05.007.

Description

Title: A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling
Author/s:
  • García, A.G.
  • Hernandez Medina, Miguel Angel
  • Perez Villalon, Gerardo
  • Portal Ruiz, Alberto
Item Type: Article
Título de Revista/Publicación: Linear Algebra And Its Applications
Date: 2011
ISSN: 0024-3795
Volume: 435
Subjects:
Freetext Keywords: Sampling in shift-invariant spaces; Smith canonical form; Matrix pencils; Kronecker canonical form; GUPTRI form
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

More information

Item ID: 11505
DC Identifier: http://oa.upm.es/11505/
OAI Identifier: oai:oa.upm.es:11505
DOI: 10.1016/j.laa.2011.05.007
Official URL: http://www.sciencedirect.com/science/article/pii/S0024379511004125
Deposited by: Memoria Investigacion
Deposited on: 25 Jul 2012 10:58
Last Modified: 20 Apr 2016 19:33
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