Design of infinite impulse response maximally flat stable digital filter with low group delay

Maximally flat digital filters (MFDFs) are widely applied in applications where the energy of useful signals is concentrated around some specific frequencies. A typical design method of MFDFs is to impose constraints on the filter's frequency response and its first- to high-order derivatives at some frequencies and to fully determine the filter coefficients from these constraints. However, infinite impulse response (IIR) MFDFs that are designed by the method are not necessarily stable or may have heavy magnitude overshoots, especially when the desired group delay is low. To overcome this shortcoming, a stability constraint that is characterized by the maximum pole radius is also imposed on the filters in this paper, resulting in IIR maximally flat stable digital filters (MFSDFs). An algorithm is presented for the design of the flatness and pole-radius constrained IIR filters with specified group delay. Using the proposed method, low-pass, high-pass, band-pass and band-stop IIR MFSDFs with low group delay have been designed. Results demonstrate the effectiveness of the proposed method and the superior performance of the IIR MFSDFs over existing MFDFs.