Abstract



The aim of this work is to solve a question raised for average sampling in shiftinvariant spaces by using the wellknown 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

00243795 
Impact factor JCR

1,005 
Impact info


Volume

435 


Journal number


From page

2837 
To page

2859 
Month

SIN MES 
Ranking
