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 23%$$ 23\% $$ of adders compared with other low complexity filter design method, which reduces effectively the implementation cost. This paper proposes a novel design algorithm for low complexity sparse 2-D FIR filters. Necessary filter coefficients are obtained by a sparse algorithm and quantized through CSD representation. Then new coefficients are reconstructed with the common subexpressions searched by CSE, which reducing the logical operations required for implementation. image