Frequency Transformations in Filter Design

The problem of determining the possible functions , that will transform the amplitude characteristic of a given network to the amplitude characteristic of another network, is considered. It is shown that the general form of these transformations is given by , where is a positive rational function of . The network function whose amplitude characteristic is is determined from the original network and the function . The concept of frequency transformations is used in filter design and network analysis; the Butterworth and Tchebycheff filters result as special forms of such transformations.