An inverse scattering approach to the partial realization problem

We present a inverse scattering interpretation of the classical minimal partial realization problem posed in a slightly generalized context. Our approach starts by considering a canonical cascadeform structure for the realization of arbitrary transfer functions Where the cascade structure can be interpreted as the description of a layered wave scattering medium. In this context the partial realization problem calls for a recursive layer identification from the input-output or scattering data. The realization algorithm operates on a pair of infinite sequences and uses a causality principle to progressively determine the parameters of the cascaded linear 2-ports that model the successive wave-interaction layers. This method turns out to fit nicely into a general framework that can also be used to obtain fast, structured linear estimation algorithms and cascade realizations for digital filters.