An efficient algorithm for constrained least-square design of quadrantally symmetric two-dimensional fir filters

A key problem for optimal design of two-dimensional (2-D) finite impulse response (FIR) filters is the efficiency of the design algorithm. Most existing algorithms have low computational efficiencies since they rearrange the coefficient matrix of a 2-D FIR filter into a vector and then solve for the coefficient vector using design algorithms for one-dimensional (1-D) FIR filters. Some 2-D based algorithms for least-square (LS) and weighted LS designs of 2-D FIR filters are very efficient because they directly compute or update the coefficient matrices of the filters. This paper considers the constrained LS (CLS) design of quadrantally symmetric 2-D FIR filters and presents a computationally efficient algorithm for the design. This algorithm generalizes the 2-D based LS design algorithm by imposing constraints on the magnitude response error of the filter such that it can efficiently solve the CLS design problems of the 2-D FIR filters. The algorithm can also be regarded as an extension of the projected LS algorithm for the CLS designs of 1-D FIR filters. Design examples and comparisons with existing algorithms demonstrate the efficiency of the proposed algorithm.