Approximation of multivariable functions by M-D transfer functions with separable denominator

The approximation of a given function by a rational function has been considered extensively by mathematicians. A particular result has been stated by Walsh that the best approximation of a given analytical function is one which interpolates the given function at several properly chosen points. In this paper, transfer functions of multidimensional digital filters with separable denominator are used for the approximation of given multivariate functions. It is shown that the result of Walsh can be generalized in a straightforward manner. By an example it is illustrated how the new result can be applied to, e.g., the order reduction of a higher-order system. In the conclusion we state the usefulness and the limitation of the result.