Low-Complexity 2-D Digital FIR Filters Using Polyphase Decomposition and Farrow Structure

This paper proposes a novel realization technique for quadrantally symmetric 2-D finite impulse response filters with a guaranteed reduction in the hardware complexity. Here, the concept of Farrow structure-based interpolation filter design using the polyphase decomposition of the 1-D filter transfer function is effectively utilized in the 2-D domain. The proposed 2-D filter makes use of row-wise polyphase decomposition of the 2-D transfer function or frequency response, followed by the polynomial approximation of the individual polyphase coefficients resulting in Farrow structures corresponding to each row filter. The final coefficients are implemented by varying the delay values in all the Farrow structures, followed by the interpolation of the coefficients obtained from each delay value, which in turn forms the rows in the 2-D kernel. The major highlight of the proposed method is the highly reduced implementation complexity in terms of the number of multipliers and adders, with a low normalized root-mean-square error. Design examples of the circularly symmetric and fan-type filters have been considered to show the efficiency of the approach. The results show a drastic reduction in the implementation complexity of the 2-D filters of upto 20%, with significantly low normalized root-mean-square error lesser than 0.5%.