Split forms of z-domain algorithms for linear prediction and stability analysis

Many algorithms in linear prediction and stability analysis may be expressed by the same general two-term recursion involving two polynomials of consecutive degrees and the reciprocated polynomial of one of them. The properties of these algorithms are interpreted from a geometrical point of view that refers to the loci described by the zeros of the polynomials in the related sequences as a characteristic real parameter varies. An analysis of all possible threeterm (split) forms involving only the symmetric and/or the antisymmetric parts of three consecutive polynomials generated by the same two-term recursion, is carried out.