Synthesis of ARMA filters by real lossless digital lattices

A new method is presented to obtain degree-one or real degree-two transfer scattering matrices of two-port lossless lattice filters through the use of complex Richard´s function extractions for the minimum degree cascade synthesis of real, stable, single-input, single-output ARMA (n, m) filters from the transfer function or the input reflection coefficient. The method relies on a four-step Richard´s function extraction where two steps are used for reducing the degree of the transfer function and two for obtaining real lattices. We treat the cases where the zeros of transmission are inside and outside the unit circle but not on the unit circle