A fast matrix iterative algorithm for WLS design of 2-D linear-phase FIR filters

The weighted least square (WLS) design of two-dimensional (2-D) linear-phase finite impulse response (FIR) filters with quadrantally symmetric or anti-symmetric magnitude responses is studied in this paper. Firstly, the necessary and sufficient condition for minimizing the WLS error is obtained in the form of matrix equation. Based on the matrix equation, a novel algorithm is derived for the WLS design of 2-D filters with two-valued weighting functions. Further, convergence of the algorithm is established and the computational complexity is analyzed. Because the new algorithm deals with the filter parameters in their natural 2-D form and the transition band is not sampled, the amount of computation required is reduced significantly, especially for high order cases. Finally, examples are presented to illustrate the performance of the proposed algorithm.