Design of maximally flat IIR filters with flat group delay responses

Digital filters with linear phase responses, that is, constant group delay responses are needed in many applications for signal and image processing. In this paper, a novel method is proposed for designing maximally flat IIR filters with flat group delay responses in the passband. First, a system of linear equations are derived from the flatness conditions of IIR filters given in the passband and stopband, respectively. Then, a set of filter coefficients can be easily obtained by simply solving this system of linear equations. In the proposed design method, the flatness of the frequency response can be specified arbitrarily. The design of lowpass filters are described in detail, and bandpass and bandstop filters are given also. Moreover, the causality and stability of the proposed maximally flat IIR filters are examined by designing various IIR filters with different group delays. It is shown from the experimental results that the obtained maximally flat IIR filters are causal stable if the group delay is set to be larger than a specific value. Finally, some design examples are presented to demonstrate the effectiveness of the proposed maximally flat IIR filters. r 2008 Elsevier B.V. All rights reserved.