Implementation of constant phase elements using low-Q band-pass and band-reject filtering sections

This paper briefly describes possibility to use band-pass and notch filters with low quality factors for straightforward synthesis of the so-called constant phase elements. These filters connected in cascade can form desired alternation of transfer function zeroes and poles. Using proposed approach one-quarter, half and three-quarter fractional-order integrator dedicated for audio and speech applications has been derived and verified by using numerical analysis. Discovered method can be generalized to arbitrary frequency range, allowed phase error and almost any biquad topology.