On the design of complementary filters

An algorithm is presented for synthesizing lowpass and highpass filters with identical phase transfer functions and such that the sum of the corresponding amplitude transfer functions is identically 1.0. The design procedure is based on model lowpass filters such as Butterworth, Chebychev, or elliptic. The complementary filters are seen to have the same pole locations as the model filters, with zero locations determined by both the poles and zeros of the models. Examples of both continuous-time and discrete-time designs are given to illustrate the method. These filters find application in the spectral decomposition of signals and in the reconstruction of physical data which have been obtained from multiple-transducer measurements.