On complex parameterizations of real rational functions

A standard construction from network theory allows the unique parameterization of real rational transfer functions by complex allpass functions of the same degree. A refinement of this construction leads to a homeomorphism, referred to as the Segal transform, between complex transfer functions of McMillan degree n and real rational transfer functions of degree 2n with Cauchy index zero. In this paper the Segal transform is described by means of state space realizations. A new class of signature symmetric realizations is desribed, and a novel parameterization of Cauchy index zero real transfer functions by bilinear systems is given.