A novel design algorithm for low complexity sparse 2‐D FIR filters

The hardware implementation complexity of traditional two‐dimensional (2‐D) finite impulse response (FIR) filters with high order is very high. In this paper, a novel sparse 2‐D FIR filter design algorithm has been proposed by combining the common subexpression elimination technique and sparse filter design algorithms to reduce hardware implementation complexity. First, an initial 2‐D FIR filter with sparse coefficients that meets frequency‐domain specifications is obtained by the sparse filter design algorithm. Then, each filter coefficient is quantized in canonical signed digit, and the sensitivities of all weight‐two subexpressions and isolated non‐zero bits are calculated. Finally, the filter coefficients with low implementation cost are reconstructed via iteratively choosing subexpressions and isolated non‐zero bits in terms of their sensitivities. Simulation results show that the proposed algorithm saves about of adders compared with other low complexity filter design method, which reduces effectively the implementation cost.