Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries
Multidimensional Systems and Signal Processing
Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint
Multidimensional Systems and Signal Processing
Realization of 2-D linear-phase FIR filters by using thesingular-value decomposition
IEEE Transactions on Signal Processing
Weighted least mean square design of 2-D FIR digital filters: thegeneral case
IEEE Transactions on Signal Processing
Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions
Multidimensional Systems and Signal Processing
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High computational complexity is a major problem encountered in the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters. In this paper, we present an iterative matrix solution with very low complexity to the weighted least square (WLS) design of 2-D quadrantally symmetric FIR filters with two-valued weighting functions. Firstly, a necessary and sufficient condition for the WLS design of 2-D quadrantally symmetric filters with general nonnegative weighting functions is obtained. Then, based on this optimality condition, a novel iterative algorithm is derived for the WLS design problem with a two-valued weighting function. Because the filter parameters are arranged in their natural 2-D form and the transition band is not sampled, the computation amount of the proposed algorithm is reduced significantly, especially for high-order filters. The exponential convergence of the algorithm is established, and its computational complexity is estimated. Design examples demonstrating the convergence rate and solution accuracy of the algorithm, as well as the relation between the iteration number of the algorithm and the size and transition-band width of the filter are given.