On the WLS design of 2-D quadrantally symmetric FIR filters with arbitrary weighting functions

The weighted least square (WLS) design of two-dimensional (2-D) finite impulse response (FIR) filters with quadrantally 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 matrix iterative algorithm is derived for the WLS design of 2-D filters with arbitrary nonnegative weighting functions. Further, convergence of the algorithm is established. The new algorithm deals with the filter parameters in their natural 2-D form and the frequency grid having no samples in transition band can be used, leading to significant computational savings. Finally, several design examples and comparisons to existing algorithms are presented, which demonstrate the performance of our algorithm.