Matrix-Based Algorithms for Constrained Least-Squares and Minimax Designs of 2-D Linear-Phase FIR Filters
Matrix-Based Algorithms for Constrained Least-Squares and Minimax Designs of 2-D Linear-Phase FIR Filters
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DOI：
10.1109/tsp.2013.2262683
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发表时间：
2013-07
影响因子：
5.4
通讯作者：
Xiaoying Hong;Xiaoping Lai;Ruijie Zhao
中科院分区：
文献类型：
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作者：
Xiaoying Hong;Xiaoping Lai;Ruijie Zhao
二维有限冲激响应滤波器的冲激响应系数本质上是一个矩阵。传统的优化设计算法将滤波器的系数矩阵重新排列成向量，然后使用一维（1-D）FIR滤波器的设计算法求解系数向量。最近的一些设计算法已经利用了2-D滤波器的系数的矩阵性质，但没有结合任何约束，因此不适用于具有显式幅度约束的2-D滤波器的设计。在本文中，我们开发了一些有效的算法，利用系数的矩阵性质的约束最小二乘（CLS）和极小极大设计的正交对称2-D线性相位FIR滤波器，这两个可以制定为一个优化问题或转换成一系列的子问题，正定二次成本和有限数量的线性约束表示在滤波器的系数矩阵。设计实例和与几种现有算法的比较表明了所提算法的有效性和效率。
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.