  We present a method able to recover location and residue of poles of
functions meromorphic in a half--plane from samples of the function on the real
positive semi-axis. The function is assumed to satisfy appropriate asymptotic
conditions including, in particular, that required by Carlson's theorem. The
peculiar features of the present procedure are: (i) it does not make use of the
approximation of meromorphic functions by rational functions; (ii) it does not
use the standard methods of regularization of ill-posed problems. The data
required for the determination of the pole parameters (i.e., location and
residue) are the approximate values of the meromorphic function on a finite set
of equidistant points on the real positive semi-axis. We show that this method
is numerically stable by proving that the algorithm is convergent as the number
of data points tends to infinity and the noise on the input data goes to zero.
Moreover, we can also evaluate the degree of approximation of the estimates of
pole location and residue which we obtain from the knowledge of a finite number
of noisy samples.
