Complementary IIR digital filter banks

The class of digital filter pairs satisfying two types of complementary properties simultaneously is reexamined. The pair is required to have complementary square magnitude characteristics with respect to a constant and transfer functions complementary with respect to an allpass function. This filter class, called doubly complementary filters is then extended to have M filters with complex outputs. Basic properties of the filters are discussed. It is shown that all the filters in the bank can be implemented as linear combinations of the same low order allpass filters. The individual filters can have different bandwidths and tolerances. The filter bank can also produce [M/2]+1 real outputs with allpass complementary responses that can be arbitrarily added up to form a variety of allpass complementary filters. The filters have low coefficient sensitivities in their passbands if the allpass sections are implemented with structures that are canonic with respect to the coefficients.