Optimal Design of Nonlinear-Phase FIR Filters With Prescribed Phase Error
Optimal Design of Nonlinear-Phase FIR Filters With Prescribed Phase Error
复制标题
具有规定相位误差的非线性相位FIR滤波器的优化设计
DOI：
10.1109/tsp.2009.2021639
复制
发表时间：
2009-09-01
影响因子：
5.4
通讯作者：
Lai, Xiaoping
中科院分区：
文献类型：
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作者：
Lai, Xiaoping
本文用统一的半无限正定二次规划方法研究了一维和二维具有给定相位误差的非线性相位FIR滤波器的约束最小二乘设计和约束切比雪夫设计。为了得到唯一的最优解，我们提出了对复逼近误差和相位误差施加约束。通过引入Sigmoid相位误差约束界函数，可以大大减小群延时误差。给出了一种基于Goldfarb-Idnani的算法来求解由约束最小二乘问题产生的半无限正定二次规划，并将其应用于约束Chebyshev设计问题，证明了该算法与半无限正定二次规划是等价的。通过设计实例，将该方法与现有的几种方法进行了比较。仿真结果验证了该方法的有效性和高效性。
Constrained least-squares design and constrained Chebyshev design of one-and two-dimensional nonlinear-phase FIR filters with prescribed phase error are considered in this paper by a unified semi-infinite positive-definite quadratic programming approach. In order to obtain unique optimal solutions, we propose to impose constraints on the complex approximation error and the phase error. By introducing a sigmoid phase-error constraint bound function, the group-delay error can be greatly reduced. A Goldfarb-Idnani based algorithm is presented to solve the semi-infinite positive-definite quadratic program resulting from the constrained least-squares design problem, and then applied after some modifications to the constrained Chebyshev design problem, which is proved in this paper to be equivalent also to a semi-infinite positive-definite quadratic program. Through design examples, the proposed method is compared with several existing methods. Simulation results demonstrate the effectiveness and efficiency of the proposed method.