  Unconstrained partial-wave amplitudes obtained at discrete energies from fits
to complete sets of eight independent observables which are required to
uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and
are in principle non-unique. We demonstrate how this behavior can be ascribed
to the continuum ambiguity. Starting from the spinless scattering case, we
demonstrate how an unknown overall phase depending on energy and angle mixes
the structures seen in the associated partial-wave amplitudes making the
partial wave decomposition non-unique, and illustrate it on a simple toy model.
We then apply these principles to pseudo-scalar meson photoproduction and show
that the non-uniqueness effect can be removed through a phase rotation
generating "up-to-a-phase" unique set of SE partial wave amplitudes. Extracting
pole positions from partial wave amplitudes is the next step. Up to now, there
was no reliable way to extract pole parameters from SE partial waves, but a new
and simple single-channel method (Laurent + Pietarinen expansion) applicable
for continuous and discrete data has been recently developed. It is based on
applying the Laurent decomposition of partial wave amplitude, and expanding the
nonresonant background into a power series of a conformal-mapping, quickly
converging power series obtaining the simplest analytic function with
well-defined partial wave analytic properties which fits the input. The
generalization of this method to multi- channel case is also developed and
presented. Unifying both methods in succession, one constructs a model
independent procedure to extract pole parameters directly from experimental
data without referring to any theoretical model.
