On diagonally weighted conformal mapping

We want to apply -plane methods for polynomial matrix spectral factorization. The usual conformal mapping transformation of a parahermitian and positive polynomial matrix to a parareciprocal trigonometric polynomial matrix leads to the introduction of zeros on the unit circle at , iff has a singular highest degree matrix coefficient. This is avoided by requiring first to be diagonally reduced, [2], [3], and then performing a new diagonally weighted conformal mapping transformation. There results a parareciprocal and positive trigonometric polynomial matrix which is better conditioned for spectral factorization than . An example illustrates the improved application of -plane methods for getting a spectral factor of .