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We introduce a polynomial filter structure for filter-and-sum beamforming applied to a microphone array application. The structure is a multidimensional extension of the well known Farrow structure, which has mainly been used for fractional delay filtering and interpolation of I-D signals. The proposed method enables an easy, smooth and efficient control of the beamforming filter characteristics by adjusting only a single control variable, e.g., for dynamic beam steering. The optimization method for polynomial beamforming filter design is presented and illustrated with simulations of beamforming filter characteristics. The design example is given for a linear array of four omni-directional microphones and a polynomial FIR filter with 20-tap delay lines.