ON COMPLEX PARAMETERIZATIONS OF REAL RATIONAL FUNCTIONS

A standard construction from network theory allows the unique paramete rization of real rational transfer functions by complex all pass funct ions of the same degree. A refinement of this construction leads to a homeomorphism, referred to as the Segal transform, between complex tra nsfer functions of McMillan degree n and real rational transfer functi ons of degree 2n with Cauchy index zero. In this paper the Segal trans form is described by means of state space realizations. A new class of signature symmetric realizations is desribed, and a novel parameteriz ation of Cauchy index zero real transfer functions by bilinear systems is given.