On biorthogonality of Hermitian and skew-Hermitian Szego/Levinson polynomials

A system of polynomials, biorthogonal with respect to a given weight function which is not necessarily even, is constructed from a corresponding system of Szego or Levinson polynomials. Two-term coupled recurrences are presented for the biorthogonal polynomial system, and it is shown that these recurrences reduce to a pair of three-term uncoupled recurrences in the case that the unit circle weight function is even. Several observations relative to recent linear prediction algorithms utilizing Hermitian and skew-Hermitian Levinson polynomials are discussed