Inverse scattering and minimal partial realizations

Abstract

We present an inverse scattering interpretation of the classical minimal partial realization problem posed in a slightly generalized context. Our approach starts by considering a canonical cascade-form 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 process of layer identification from a given input-response pair (the scattering data). The realization algorithm uses a causality principle to progressively determine the parameters of cascaded linear 2-ports that model the successive wave-interaction layers. This method for approaching the realization problem turns out to fit nicely into a framework that was also used to obtain fast, structured linear estimation algorithms and cascade realizations for digital filters.