A new mathematical theory of wave filters gives the following results: It is possible to realize as constant an image impedance as desired in the transmitting bands. In the new theory there is no mathematical difference in the consideration of proper attenuation or proper image impedance characteristics. In other words, the same attack applies in both cases. All known wave filters as far as they are symmetrical fourterminal networks or equivalent to such networks in series with a transformer, are contained in the filters of the new theory which comprises all possible filters of this kind. The new theory has been carried through practically to find out the most economical filter for any practical purpose. This results in many cases in solving a given practical question already solved by known methods with considerable saving of material. The chief aim of this paper is to show the relation between the new theory and the older design methods due to O. J. Zobel and other members of the Bell Laboratories.