Closed-form design of maximally flat IIR half-band filters

In this paper, a new closed-form expression for the transfer function of the maximally flat (MF) IIR half-band (HB) filters is presented. The filter coefficients are directly obtained by solving a linear system of Vandermonde equations that are derived from the maximal flatness conditions. The proposed IIR half-band filters are more general than the existing half-band filters, because they include the conventional FIR half-band filters with exactly linear phase, the generalized FIR half-band filters with approximately linear phase; and the allpass-based IIR half-band filters, as special cases. Furthermore, the IIR HB filters with exactly linear phase and the causal stable IIR HB filters can be realized also. Finally, some design examples are presented to demonstrate the effectiveness of the proposed IIR HB filters.