On the synthesis of multidimensional reactance multiports

Multidimensional lossless networks are of interest, for example, for use as reference filters for multidimensional wave digital filters. Necessary properties of the scattering matrix of such multiports have been established. In the design of k-dimensional reactance networks it is of great interest whether these mentioned features are also sufficient for a given matrix to be the scattering matrix of such a system, or not. It is shown that this is not the case for dimensions greater than two. Hence, no general synthesis procedure for multidimensional reactance multiports exists, as is in the one- and two-dimensional cases