Forward and inverse scattering for discrete layered lossy and absorbing media

A complete digital signal processing (DSP) theory is developed for forward and inverse scattering in discrete (piecewise-constant) layered lossy systems, generalizing previous work for discrete lossless systems and continuous lossy systems. This paper is motivated by radar reflections from stratified dielectrics and interchip communication modeled by lossy transmission lines. The DSP formulation allows exact solutions, without discretization approximations, and includes all multiple reflections, transmission scattering losses, and absorption effects. For the forward problem, discrete matrix Green's functions are derived for the lossy medium, as are fast algorithms for computing impulse reflection and transmission responses for the medium. For the inverse problem, asymmetric Toeplitz systems of equations which function as discrete counterparts to integral equations are derived, as are fast algorithms for reconstructing the medium from its impulse transmission and reflection responses. Data sufficiency and feasibility are discussed. Finally, these results are applied to the LCRG transmission line and layered dielectric medium problems, dispersion effects are discussed, and a numerical example is presented.