  Assume that samples of a filtered version of a function in a shift-invariant
space are avalaible. This work deals 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. This is done in the light of the generalized sampling theory by
using the oversampling technique: more samples than strictly necessary are
used. For a suitable choice of the sampling period, a necessary and sufficient
condition is given in terms of the Kronecker canonical form of a matrix pencil.
Comparing with other characterizations in the mathematical literature, the
given here has an important advantage: it can be reliable computed by using the
GUPTRI form of the matrix pencil. Finally, a practical method for computing the
compactly supported reconstruction functions is given for the important case
where the oversampling rate is minimum.
