  The matrix pencil method (MPM) is a well-known technique for estimating the
parameters of exponentially damped sinusoids in noise by solving a generalized
eigenvalue problem. However, in several cases, this is an ill-conditioned
problem whose solution is highly biased under small perturbations. When the
estimation is performed to classify the observed signal into two categories,
the estimation errors induce several misclassifications. In this work we
propose a novel signal classification criteria by exploiting the relationship
between the generalized eigenvalue problem posed in the MPM and the numerical
range of a pair of rectangular matrices. In particular, the classification test
is formulated as a set inclusion problem, and no spectrum estimation is
required. The technique is applied to a problem of electromagnetic scattering
to classify dielectric materials using the scattering signal observed when a
target is illuminated by an ultra-wideband signal. The performance of the
classification scheme is assessed in terms of error rate and it is compared to
another classification technique, the generalized likelihood rate test (GLRT).
