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Pole-polynomial decomposition forms the basis for classifying active filters into ten groups. This classification serves two purposes. First, the gain and sensitivity properties are directly related to the type of decomposition. Thus the optimum gain and sensitivity values for any filter structure can be easily determined by simply finding the classification to which the filter belongs. Second, active filters have been developed for two new types of polynomial decomposition for which no active filters previously existed. These new circuits have very good gain-sensitivity properties.