RATIONAL MULTIPLE CRITERION APPROXIMATION AND RATIONAL COMPLEX APPROXIMATION BY DIFFERENTIAL CORRECTION-TYPE ALGORITHMS

This work shows how to extend the differential correction algorithm (a well-known technique for rational minimax approximation of real funct ions) to handle simultaneous minimax approximation of magnitude and ph ase of complex-valued functions defined on the unit circle of the comp lex plane. The proposed procedure enjoys global convergence to local b est approximants with poles only inside the unit circle. Hence, the ap proximants obtained can be used as transfer functions of causal and st able linear systems, and the proposed technique can be profitably appl ied to digital filter design. The differential correction strategy can also be applied to rational complex approximation, and can also be ex tended to the case of multidimensional rational functions, retaining t he properties of the one-dimensional case. This ability to produce sta ble transfer functions is of special interest in the multidimensional case.