  We pose the deterministic, nonparametric, approximation problem for scalar
nonnegative input/output systems via finite impulse response convolutions,
based on repeated observations of input/output signal pairs. The problem is
converted into a nonnegative matrix factorization with special structure for
which we use Csisz\'ar's I-divergence as the criterion of optimality.
Conditions are given, on the input/output data, that guarantee the existence
and uniqueness of the minimum. We propose a standard algorithm of the
alternating minimization type for I-divergence minimization, and study its
asymptotic behavior. We also provide a statistical version of the minimization
problem and give its large sample properties.
