Memorias de investigación
Research Publications in journals:
A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling
Year:2011
Research Areas
  • Physics chemical and mathematical
Information
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 the- ory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the func- tion 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 reconstruc- tion functions with compact support. Thus, low computational com- plexity 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 origi- nal problem reduces to finding a polynomial left inverse of a polyno- mial 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. More- over, the optimality of the obtained solution is established.
International
Si
JCR
Si
Title
Linear Algebra And Its Applications
ISBN
0024-3795
Impact factor JCR
1,005
Impact info
Volume
435
Journal number
From page
2837
To page
2859
Month
SIN MES
Ranking
Participants
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Grupo de Sistemas Dinámicos, Aprendizaje y Control (SISDAC)