Transitional Butter–Elliptic filter suitable for complementary decomposition

Abstract

Direct synthesis of recursive digital filters, whose characteristic function belongs to the new IIR filters class, is described in this article. Attenuation characteristic in the passband lies between the Butterworth's and the Elliptic's attenuation characteristics. All zeros of transfer function are placed on the unit circle so that the condition for complementary decomposition is fulfilled. Complementary decomposition into parallel connection of two allpass filters is performed. Then, lowpass filter is obtained summing these two filters and its complementary highpass filter – by their subtraction. The main advantage of this kind of filters is its smaller sensitivity to digital word length change compared to standard filters.