SYNTHESIS OF Two - DIMENSIONAL LOSSLESS m - PORTS WITH PRESCRIBED SCATTERING MATRIX

Multidimensional lossless networks are of special interest for use as reference structures for multidimensional wave digital filters [1]-[3]. The starting point of the presented synthesis procedure for two-dimensional representatives of the networks mentioned is a scattering matrix description of the desired multiport. This given matrix is assumed to have those properties which have turned out to be necessary [9], [ 10] for any scattering matrix of a multidimensional lossless network. The method presented for the synthesis of 2-D reactance m-ports is based mainly on known properties of block-companion matrices and the factorization of a univari-able rational matrix which is discrete para-Hermitian and nonnegative definite on the unit circle. The resulting network always contains only a minimal number of frequency-dependent building elements. No restrictions are made concerning the coefficients of the rational entries of the scattering matrix; they may be either real or complex, so as to include even complex networks which are of special interest for multi-dimensional wave digital filters [3].