Matrix-Based Algorithms for Constrained Least-Squares and Minimax Designs of 2-D Linear-Phase FIR Filters

Abstract

The impulse response coefficients of a two-dimensional (2-D) finite impulse response (FIR) filter are in a matrix form in nature. Conventional optimal design algorithms rearrange the filter's coefficient matrix into a vector and then solve for the coefficient vector using design algorithms for one-dimensional (1-D) FIR filters. Some recent design algorithms have exploited the matrix nature of the 2-D filter's coefficients but not incorporated with any constraints, and thus are not applicable to the design of 2-D filters with explicit magnitude constraints. In this paper, we develop some efficient algorithms exploiting the coefficients' matrix nature for the constrained least-squares (CLS) and minimax designs of quadrantally symmetric 2-D linear-phase FIR filters, both of which can be formulated as an optimization problem or converted into a sequence of subproblems with a positive-definite quadratic cost and a finite number of linear constraints expressed in terms of the filter's coefficient matrix. Design examples and comparisons with several existing algorithms demonstrate the effectiveness and efficiency of the proposed algorithms.

DOI: 10.1109/TSP.2013.2262683

11 Figures and Tables

Cite this paper

@article{Hong2013MatrixBasedAF, title={Matrix-Based Algorithms for Constrained Least-Squares and Minimax Designs of 2-D Linear-Phase FIR Filters}, author={Xiaoying Hong and Xiaoping Lai and Ruijie Zhao}, journal={IEEE Transactions on Signal Processing}, year={2013}, volume={61}, pages={3620-3631} }