Power-complementary IIR filter pairs with an adjustable crossover frequency

This paper introduces two classes of power-complementary recursive low-pass/high-pass filter pairs with an adjustable crossover frequency in such a way that the stopband attenuation of both filters remains the same. For each class, the filter pair is constructed using two all-pass sub-filters as building blocks. Based on the properties elliptic minimal Q-factors transfer functions, simple expressions are derived for evaluating the coefficients in all-pass sections in order to achieve the desired crossover frequency. The design procedures are developed for synthesizing power-complementary filter pairs implemented as a parallel connection of two all-pass sub-filters and for the tapped cascaded interconnections of two identical all-pass sub-filters. The direct parallel connection has both the power-complementary and all-pass complementary property. The second class of filters constructed using several identical copies of the two all-pass filters possesses the power-complementary property.