基于拉格朗日乘子法的二维修正DFT调制滤波器组设计算法

周芳; 水鹏朗; 蒋俊正

doi:10.11999/JEIT160651

基于拉格朗日乘子法的二维修正DFT调制滤波器组设计算法

doi: 10.11999/JEIT160651

2.
(西安电子科技大学雷达信号处理国家重点实验室西安 710071) ②(桂林电子科技大学生命与环境科学学院桂林 541004) ③(桂林电子科技大学信息与通信学院桂林 541004)

基金项目:

国家自然科学基金(61261032)

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出版历程
- 收稿日期: 2016-06-21
- 修回日期: 2016-11-28
- 刊出日期: 2017-05-19

Design of Two-dimensional Modified DFT Modulated Filter Banks Based on Lagrange Multiplier Method

2.
(National Laboratory of Radar Signal Processing, Xidian University, Xi&rsquo

Funds:

The National Natural Science Foundation of China (61261032)

摘要

摘要: 基于拉格朗日乘子法，该文提出一种2维修正离散傅里叶变换调制滤波器组的迭代设计方法。在每次迭代中，原型滤波器的设计描述成一个约束为2次函数的2次规划问题。引入拉格朗日乘子法将问题转化为无约束的优化问题，通过求解线性矩阵方程得到优化问题的解。针对矩阵方程中的系数矩阵的特点，运用块LU分解，显著降低了运算复杂度。仿真实验表明，与现有的设计方法相比，该文方法设计得到的2维修正离散傅里叶变换调制滤波器组的重构误差和阻带衰减均有较大的改善。
- 2维修正滤波器组 /
- 离散傅里叶变换调制 /
- 迭代优化 /
- 拉格朗日乘子法 /
- 块LU分解
Abstract: Base on Lagrange multiplier method, an iterative algorithm is proposed to design the two-dimensional modified Discrete Fourier Transform (DFT) modulated filter bank. In each iteration, the design problem is described as a Quadratically Constrained Quadratic Program (QCQP). The Lagrange multiplier method is then employed to transform the constrained problem into an unconstrained one, the solution of which is obtained by solving a set of linear equations. By analyzing the coefficient matrix, block LU factorization is applied to considerably reduce the computational complexity. Numerical results and comparison with the existing methods demonstrate the improved performance of the proposed scheme, including the reconstruction error and stopband attenuation.
- Two-dimensional modified filter bank /
- DFT modulated /
- Iteration optimization /
- Lagrange multiplier method /
- Block LU factorization

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参考文献(19)

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