Three classes of IIR complementary filter pairs with an adjustable crossover frequency

Three classes of complementary recursive low-pass/high-pass filter pairs are introduced. For each class, the crossover frequency can be arbitrarily selected without changing the predetermined stop-band attenuation being the same for both filters and the filter pair is constructed using two all-pass subfilters as building blocks. Based on the properties of elliptic minimal Q-factors transfer functions, simple expressions are derived for evaluating the coefficients for the all-pass sections to arbitrarily change the crossover frequency. Design procedures are developed for synthesizing filter pairs implemented as a parallel connection of two all-pass sub-filters and for two classes of filter pairs constructed as tapped cascaded interconnections of two identical all-pass sub-filters. The first of them together with the direct parallel connection of two all-pass filters provide the power-complementary property, whereas the second one provides the magnitude-complementary property.