A new (numerical) method is described to determine all coupled mode parameters of a complex plasmon-phonon system in a semiconductor. First a general theoretical description is given of the complex dielectric function describing such a system. Some paractically important relations are deduced. Starting from an experimentally determined reflectivity spectrum, the dielectric function is determined at a number of discreate frequencies by means of Kramers-Kronig analysis. A complete background is given for a numerical method to determine all relevant mode parameters, especially the coordinates of poles and zeros in the complex frequency plane, from this spectrum. Finally the new method is applied to a test spectrum. The results are discussed and compared with those of other methods.