Descripción
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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. | |
Internacional
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Si |
JCR del ISI
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Si |
Título de la revista
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Linear Algebra And Its Applications |
ISSN
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0024-3795 |
Factor de impacto JCR
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1,005 |
Información de impacto
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Volumen
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435 |
DOI
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Número de revista
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Desde la página
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2837 |
Hasta la página
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2859 |
Mes
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SIN MES |
Ranking
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