Efficient 1D and circular symmetric 2D FIR filters with variable cutoff frequencies using the Farrow structure and multiplier-block

This paper proposes new structures for realizing ID and circular symmetric 2D FIR filters with variable cutoff frequencies. They are based on the interpolation of the impulse responses using the Farrow structure. The coefficients of the sub-filters in the Farrow structure are represented in sum-of-powers-of-two (SOPOT) coefficients, which can easily be implemented as simple shifts and additions. Furthermore, using the transposed form realization of the sub-filters, all the SOPOT coefficients can be implemented by a single multiplier-block exploiting the redundancy among the SOPOT coefficients. Several design examples are given to demonstrate the effectiveness and feasibility of the proposed approach.