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Design of elliptic IIR filters with a reduced number of shift-and-add operations in multipliers

In this paper, a new design method for IIR digital filters which provides the implementation of a half of multiplication constants with few shifters and adders is proposed. The transfer function is developed from an elliptic minimal Q-factors analog prototype and the realization is based on the parallel connection of two allpass networks. In all second order sections of the parallel branches, the digital filter has one common constant independent of the filter order and transition bandwidth. The value of the constant depends only on the frequency for which the filter attenuation is 3 dB and may be adjusted according to the predetermined number of shift-and-add operations.