New connections between asymmetric Toeplitz matrix algorithms and inverse scattering

Several fast algorithms for the recovery of the impedance and reflection coefficients of a discrete asymmetric lossy medium are presented. The data required are the reflection response to an impulsive input on the surface, and the transmission response to an impulsive input incident from below. It is shown that these efficient algorithms are related to the generalized Levinson algorithm, the Schur algorithm, and the QR lattice algorithm for solutions of symmetric and asymmetric Toeplitz matrices equations. These unified, conceptual connections aid in the understanding of the symmetric and asymmetric Toeplitz matrix algorithms in the linear prediction literature