A New Separable Two-dimensional Finite Impulse Response Filter Design With Sparse Coefficients

The separable two-dimensional (2-D) finite impulse response (FIR) filter can be utilized to decrease the implementation complexity of the traditional 2-D FIR filter. A novel separable 2-D FIR filter design is proposed in this paper. The proposed design deals with a submatrix of the prototype 2-D FIR filter coefficient matrix, which contains all the information of the filter coefficient matrix. And, its basic idea is to try to utilize some column vectors of the submatrix itself to decompose this submatrix. There are zero-valued and/or one-valued coefficients in the proposed filter. In the filter implementation, these zero-valued coefficients do not require multipliers or adders. And, these one-valued coefficients do not require multipliers. Additionally, an optimal design of the general separable 2-D FIR filter in the mini-max sense and the least-square sense in the frequency domain is provided in a uniform framework, for the first time. Finally, the experimental comparison of the proposed separable 2-D FIR filter design with other separable 2-D FIR filter designs, and the comparison with other non-separable-structure low-complexity 2-D FIR filter designs are provided to validate the superiority of the proposed method.