  We consider the problem of ``algebraic reconstruction'' of linear
combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier
samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of
the common set of zeroes of the Fourier transforms ${\cal F}(f_\l), \ \l \ne
r$, on which ${\cal F}(f_r)\ne 0$. We show that in this way the reconstruction
system is reduced to $k$ separate systems, each including only one of the
signals $f_r$. Each of the resulting systems is of a ``generalized Prony''
form. We discuss the problem of unique solvability of such systems, and provide
some examples.
