Design of IIR filters using new three allpass filters structure

We present a new structure for the IIR filter design composed of three allpass filters, i.e., one real-valued and two complex-valued allpass filters. In particular, applying the inverse discrete Fourier transform to the allpass filters, we get three real doubly complementary IIR filters. We also provide the procedure to design a lowpass filter with a desired characteristic using a complex-valued allpass filter with pre-determined characteristics. The proposed structure is used for three different lowpass filter designs, that is, eigenfilter, equiripple, and maximally flat filter design. Closed form equations for the computation of the maximally flat filter coefficients are also provided. The design techniques are illustrated by means of examples.