Multidimensional rational modeling from specified frequency response samples

Summary form only given, as follows. Given certain frequency response samples or, equivalently, the values of the linear multidimensional system transfer function at specified points on the unit torus, the objective is to obtain a rational model for the system by identifying its transfer function. The authors set up the calculus for multivariate divided differences with the objective of using it to supply a rational model for a multidimensional system from specified frequency response samples. In order to obtain the denominator polynomial, it is shown that a system of linear equations characterized by the block Hankel-Hankel matrix structure has to be targeted for solution. The numerator polynomial can then be obtained by applying multivariate Lagrangian interpolation. Some results concerning simulation are presented. Currently under investigation are procedures for recursively updating the order of the model similar to what has been established in multivariate Pade approximation theory