  It is shown that the spectral points (bound states and resonances) generated
by a central potential of a single-channel problem, can be found using rational
parametrization of the S-matrix. To achieve this, one only needs values of the
S-matrix along the real positive energy axis. No calculations of the S-matrix
at complex energies or a complex rotation are necessary. The proposed method is
therefore universal in that it is applicable to any potential (local,
non-local, discontinuous, etc.) provided that there is a way of obtaining the
S-matrix (or scattering phase-shifts) at real collision energies. Besides this,
combined with any method that extracts the phase-shifts from the scattering
data, the proposed rational parametrization technique would be able to do the
spectral analysis using the experimental data.
