Generalizations of classical recursive digital filters and their design with the aid of a Remez-type algorithm

The class of classical recursive digital filters is generalized such that the resulting filters are implementable using low-sensitivity and low-noise structures originally developed for classical filters. These filters can be synthesized to have several passband and stopband regions and arbitrary weightings can be used in these regions. In addition, some transmission and attenuation zeros can be fixed. An efficient algorithm is constructed for optimizing the proposed filters based on iteratively adjusting the passband and stopband responses of the filter with the aid of a Remez-type algorithm. Several examples are included illustrating the usefulness of the proposed generalized filters as well as the efficiency and flexibility of the algorithm